Pub Date : 2026-10-01Epub Date: 2026-02-22DOI: 10.1016/j.cam.2026.117491
Longfei Wang , Yong Xia , Yunhai Xiao
We address a class of optimization problems, denoted by (SFC), of minimizing the sum of a convex-concave fraction and a convex function over a convex set. It is shown that problem (SFC) can be reformulated into an equivalent one-dimensional optimization problem, where each subproblem is evaluated by solving an associated convex programming. The optimal Lagrangian multipliers of the convex subproblems are utilized to construct sawtooth-curve and wave-curve lower bounds, which play a crucial role in devising the branch-and-bound algorithm for globally solving (SFC). In this paper, we propose a two-layer dual approach to get hidden sawtooth-curve lower bounds, which leads to a new efficient branch-and-bound algorithm for solving (SFC). Moreover, we improve the iterative complexity with wave-curve bounds to for finding an ϵ-approximate optimal solution. Numerical results demonstrate that it is more efficient than the recent branch-and-bound algorithm based on wave-curve bounds.
{"title":"Global optimization of a convex-concave fraction plus a convex function using hidden sawtooth-curve bounds via a two-layer dual approach","authors":"Longfei Wang , Yong Xia , Yunhai Xiao","doi":"10.1016/j.cam.2026.117491","DOIUrl":"10.1016/j.cam.2026.117491","url":null,"abstract":"<div><div>We address a class of optimization problems, denoted by (SFC), of minimizing the sum of a convex-concave fraction and a convex function over a convex set. It is shown that problem (SFC) can be reformulated into an equivalent one-dimensional optimization problem, where each subproblem is evaluated by solving an associated convex programming. The optimal Lagrangian multipliers of the convex subproblems are utilized to construct sawtooth-curve and wave-curve lower bounds, which play a crucial role in devising the branch-and-bound algorithm for globally solving (SFC). In this paper, we propose a two-layer dual approach to get hidden sawtooth-curve lower bounds, which leads to a new efficient branch-and-bound algorithm for solving (SFC). Moreover, we improve the iterative complexity <span><math><mrow><mi>O</mi><mo>(</mo><mfrac><mn>1</mn><mi>ϵ</mi></mfrac><mo>)</mo></mrow></math></span> with wave-curve bounds to <span><math><mrow><mi>O</mi><mo>(</mo><mfrac><mn>1</mn><msqrt><mi>ϵ</mi></msqrt></mfrac><mo>)</mo></mrow></math></span> for finding an ϵ-approximate optimal solution. Numerical results demonstrate that it is more efficient than the recent branch-and-bound algorithm based on wave-curve bounds.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117491"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-01Epub Date: 2026-02-21DOI: 10.1016/j.cam.2026.117497
Hanjie Liu , Yuanguo Zhu , Liu He , Zihan Qin
How to reallocate the cost reasonably among participants in the production process is a research topic that attracts much attention. In this paper, a new production possibility set is defined for the first time by using chance constraint under the premise that the inputs and outputs of decision-making units (DMUs) are regarded as uncertain variables. An uncertain data envelopment analysis (DEA) model is developed to evaluate the efficiency performance of DMUs, and the model is improved to enhance its ability to distinguish efficient DMUs. Given the competitive landscape among DMUs, a cost reallocation problem based on the efficiency of DMUs is studied. Initially, we construct an optimization model aimed at maximizing DMU’s efficiency, allowing each DMU to propose an initial efficiency evaluation proposal that maximizes its own interests, which is usually not satisfied by all DMUs. Consequently, we present an uncertain bargaining game model, through which the efficiency evaluation proposals of each DMU are continuously adjusted until a consensus is reached that satisfies all DMUs. Moreover, we also provide deterministic forms for all relevant models and verify their feasibility. Then, we design a bargaining game algorithm to determine the final efficiency evaluation proposal. We prove the convergence of this algorithm and demonstrate that the obtained efficiency evaluation proposal constitutes a Nash equilibrium solution. Finally, a classic numerical example is used to illustrate the effectiveness of the proposed method. Compared with the existing efficiency evaluation methods for dealing with data uncertainty and cost allocation methods, the proposed method shows significant superiority.
{"title":"A bargaining game approach for cost reallocation within an uncertain DEA model under chance constraints","authors":"Hanjie Liu , Yuanguo Zhu , Liu He , Zihan Qin","doi":"10.1016/j.cam.2026.117497","DOIUrl":"10.1016/j.cam.2026.117497","url":null,"abstract":"<div><div>How to reallocate the cost reasonably among participants in the production process is a research topic that attracts much attention. In this paper, a new production possibility set is defined for the first time by using chance constraint under the premise that the inputs and outputs of decision-making units (DMUs) are regarded as uncertain variables. An uncertain data envelopment analysis (DEA) model is developed to evaluate the efficiency performance of DMUs, and the model is improved to enhance its ability to distinguish efficient DMUs. Given the competitive landscape among DMUs, a cost reallocation problem based on the efficiency of DMUs is studied. Initially, we construct an optimization model aimed at maximizing DMU’s efficiency, allowing each DMU to propose an initial efficiency evaluation proposal that maximizes its own interests, which is usually not satisfied by all DMUs. Consequently, we present an uncertain bargaining game model, through which the efficiency evaluation proposals of each DMU are continuously adjusted until a consensus is reached that satisfies all DMUs. Moreover, we also provide deterministic forms for all relevant models and verify their feasibility. Then, we design a bargaining game algorithm to determine the final efficiency evaluation proposal. We prove the convergence of this algorithm and demonstrate that the obtained efficiency evaluation proposal constitutes a Nash equilibrium solution. Finally, a classic numerical example is used to illustrate the effectiveness of the proposed method. Compared with the existing efficiency evaluation methods for dealing with data uncertainty and cost allocation methods, the proposed method shows significant superiority.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117497"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-01Epub Date: 2026-02-22DOI: 10.1016/j.cam.2026.117500
Nasreen Almohanna , Ali Ahmad , Khawlah Alhulwah , Ali N.A. Koam , Hamdan Alshehri
Graph theory currently encompasses the study of several subjects, ranging from algebraic features of structures to the analysis of chemical graph structures without experimental procedures. Additionally, it involves the development of networks using topological Indices (TIs). Exploring different networks and utilising TIs is an expanding field of contemporary research. The use of optoelectronic technology in optical transposition interconnection systems (OTIS) offers an effective solution to the ongoing problem of storing and sending data with comprehensive information. This is due to the reduced power requirements and broad bandwidth capabilities of optoelectronic systems, which make them well-suited for this task. The integration of radio communication and electrical technology has transformed OTIS into a highly valued network, enhancing the efficiency of existing optoelectronic computers. OTIS is characterised by the biswapped network (BN) that is formed with the help of path graph and denoted as . This research work focused on the M-polynomial and entropy measures in relation to the number of connections between nodes of the graph and its largest subgraph that preserves twin nodes ().
{"title":"Exploration of M-polynomial and entropy measures of biswapped networks with connection number approaches","authors":"Nasreen Almohanna , Ali Ahmad , Khawlah Alhulwah , Ali N.A. Koam , Hamdan Alshehri","doi":"10.1016/j.cam.2026.117500","DOIUrl":"10.1016/j.cam.2026.117500","url":null,"abstract":"<div><div>Graph theory currently encompasses the study of several subjects, ranging from algebraic features of structures to the analysis of chemical graph structures without experimental procedures. Additionally, it involves the development of networks using topological Indices (TIs). Exploring different networks and utilising TIs is an expanding field of contemporary research. The use of optoelectronic technology in optical transposition interconnection systems (OTIS) offers an effective solution to the ongoing problem of storing and sending data with comprehensive information. This is due to the reduced power requirements and broad bandwidth capabilities of optoelectronic systems, which make them well-suited for this task. The integration of radio communication and electrical technology has transformed OTIS into a highly valued network, enhancing the efficiency of existing optoelectronic computers. OTIS is characterised by the biswapped network (BN) that is formed with the help of path graph <span><math><msub><mi>P</mi><mi>m</mi></msub></math></span> and denoted as <span><math><mrow><mi>B</mi><mo>(</mo><msub><mi>P</mi><mi>m</mi></msub><mo>)</mo></mrow></math></span>. This research work focused on the M-polynomial and entropy measures in relation to the number of connections between nodes of the graph <span><math><mrow><mi>B</mi><mo>(</mo><msub><mi>P</mi><mi>m</mi></msub><mo>)</mo></mrow></math></span> and its largest subgraph that preserves twin nodes (<span><math><mrow><mi>M</mi><mo>(</mo><mi>B</mi><mrow><mo>(</mo><msub><mi>P</mi><mi>m</mi></msub><mo>)</mo></mrow><mo>)</mo></mrow></math></span>).</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117500"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, we investigate the existence of solutions for an infinite system of nonlinear (p, q)-integral equations within the framework of Banach spaces. Utilizing the concept of measure of noncompactness and Petryshyn’s fixed point theorem, we derive a set of sufficient conditions under which the system admits at least one solution. The methodology integrates the structure of generalized (p, q)-calculus with operator-theoretic techniques to handle infinite-dimensional behavior effectively. The analytical framework is complemented by illustrative examples that demonstrate the validity and applicability of the main results.
{"title":"Existence of solutions for infinite nonlinear (p, q)-integral equations","authors":"Hamid Reza Sahebi , Manochehr Kazemi , Bipan Hazarika","doi":"10.1016/j.cam.2026.117489","DOIUrl":"10.1016/j.cam.2026.117489","url":null,"abstract":"<div><div>In this work, we investigate the existence of solutions for an infinite system of nonlinear (<em>p, q</em>)-integral equations within the framework of Banach spaces. Utilizing the concept of measure of noncompactness and Petryshyn’s fixed point theorem, we derive a set of sufficient conditions under which the system admits at least one solution. The methodology integrates the structure of generalized (<em>p, q</em>)-calculus with operator-theoretic techniques to handle infinite-dimensional behavior effectively. The analytical framework is complemented by illustrative examples that demonstrate the validity and applicability of the main results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117489"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-01Epub Date: 2026-02-10DOI: 10.1016/j.cam.2026.117409
Mingrong Cui
Relaxation Crank-Nicolson compact finite difference schemes for solving both one dimensional and two dimensional Allen-Cahn equation are given and analyzed in this paper. Using the idea of relaxation scheme, that is, after introducing a new auxiliary variable, we get a newly added equation to separate the nonlinear term in the original equation. After we discretize the time derivative by Crank-Nicolson scheme with the newly introduced variable approximated on the staggered time mesh points, and approximate the second order spatial derivatives by the compact finite difference method, we obtain the fully discrete relaxation compact finite difference schemes. The linear relaxation schemes have the properties of discrete mass conservation and discrete energy dissipation. Some numerical results are provided, showing that the schemes are second order accurate in time and fourth order accurate in space, verifying the accuracy and efficiency of the proposed algorithm.
{"title":"Relaxation Crank-Nicolson compact finite difference schemes for Allen-Cahn equation","authors":"Mingrong Cui","doi":"10.1016/j.cam.2026.117409","DOIUrl":"10.1016/j.cam.2026.117409","url":null,"abstract":"<div><div>Relaxation Crank-Nicolson compact finite difference schemes for solving both one dimensional and two dimensional Allen-Cahn equation are given and analyzed in this paper. Using the idea of relaxation scheme, that is, after introducing a new auxiliary variable, we get a newly added equation to separate the nonlinear term in the original equation. After we discretize the time derivative by Crank-Nicolson scheme with the newly introduced variable approximated on the staggered time mesh points, and approximate the second order spatial derivatives by the compact finite difference method, we obtain the fully discrete relaxation compact finite difference schemes. The linear relaxation schemes have the properties of discrete mass conservation and discrete energy dissipation. Some numerical results are provided, showing that the schemes are second order accurate in time and fourth order accurate in space, verifying the accuracy and efficiency of the proposed algorithm.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117409"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-01Epub Date: 2026-02-22DOI: 10.1016/j.cam.2026.117461
Hanghang Wu , Hongqi Yang
We consider the problem of identifying the source term in an advection-dispersion equation based on given terminal data. It is shown that this is an ill-posed problem. The optimal error bound of the problem under certain source conditions is given. Then, the mollification regularization method and the Fourier regularization method are used to solve the problem respectively. Under the selection rules of a-priori and a-posteriori regularization parameters, we derive the a-priori and a-posteriori error estimates. From the theoretical derivation, it can be seen that the error estimates obtained by both regularization methods do not exhibit saturation effects, and the a-posteriori error estimate obtained by using the Fourier regularization is optimal. Finally, numerical experiments are conducted to demonstrate the effectiveness and stability of the proposed regularization methods. Additionally, comparisons between the two regularization methods are presented, along with the conclusions drawn from these comparisons.
{"title":"Optimal error bound and regularization methods for identifying an unknown source in an advection-dispersion equation","authors":"Hanghang Wu , Hongqi Yang","doi":"10.1016/j.cam.2026.117461","DOIUrl":"10.1016/j.cam.2026.117461","url":null,"abstract":"<div><div>We consider the problem of identifying the source term in an advection-dispersion equation based on given terminal data. It is shown that this is an ill-posed problem. The optimal error bound of the problem under certain source conditions is given. Then, the mollification regularization method and the Fourier regularization method are used to solve the problem respectively. Under the selection rules of a-priori and a-posteriori regularization parameters, we derive the a-priori and a-posteriori error estimates. From the theoretical derivation, it can be seen that the error estimates obtained by both regularization methods do not exhibit saturation effects, and the a-posteriori error estimate obtained by using the Fourier regularization is optimal. Finally, numerical experiments are conducted to demonstrate the effectiveness and stability of the proposed regularization methods. Additionally, comparisons between the two regularization methods are presented, along with the conclusions drawn from these comparisons.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117461"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-01Epub Date: 2025-12-24DOI: 10.1016/j.nonrwa.2025.104580
Leander Claes , Michael Winkler
<div><div>In bounded <em>n</em>-dimensional domains with <em>n</em> ≥ 1, this manuscript examines an initial-boundary value problem for the system<span><span><span><math><mtable><mtr><mtd><mrow><mo>{</mo><mtable><mtr><mtd><mrow><msub><mi>u</mi><mrow><mi>t</mi><mi>t</mi></mrow></msub><mo>=</mo><mi>∇</mi><mo>·</mo><mrow><mo>(</mo><mi>γ</mi><mrow><mo>(</mo><mstyle><mi>Θ</mi></mstyle><mo>)</mo></mrow><mi>∇</mi><msub><mi>u</mi><mi>t</mi></msub><mo>)</mo></mrow><mo>+</mo><mi>a</mi><mi>∇</mi><mo>·</mo><mrow><mo>(</mo><mi>γ</mi><mrow><mo>(</mo><mstyle><mi>Θ</mi></mstyle><mo>)</mo></mrow><mi>∇</mi><mi>u</mi><mo>)</mo></mrow><mo>+</mo><mi>∇</mi><mo>·</mo><mi>f</mi><mrow><mo>(</mo><mstyle><mi>Θ</mi></mstyle><mo>)</mo></mrow><mo>,</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mstyle><mi>Θ</mi></mstyle><mi>t</mi></msub><mo>=</mo><mi>D</mi><mstyle><mi>Δ</mi></mstyle><mstyle><mi>Θ</mi></mstyle><mo>+</mo><mstyle><mi>Γ</mi></mstyle><mrow><mo>(</mo><mstyle><mi>Θ</mi></mstyle><mo>)</mo></mrow><msup><mrow><mo>|</mo><mi>∇</mi><msub><mi>u</mi><mi>t</mi></msub><mo>|</mo></mrow><mn>2</mn></msup><mo>+</mo><mi>F</mi><mrow><mo>(</mo><mstyle><mi>Θ</mi></mstyle><mo>)</mo></mrow><mo>·</mo><mi>∇</mi><msub><mi>u</mi><mi>t</mi></msub><mo>,</mo></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></math></span></span></span>which in the case <span><math><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow></math></span> and with <em>γ</em> ≡ Γ as well as <em>f</em> ≡ <em>F</em> reduces to the classical model for the evolution of displacement and temperatures in thermoviscoelasticity. Unlike in previous related studies, the focus here is on situations in which besides <em>f</em> and <em>F</em>, also the core ingredients <em>γ</em> and Γ may depend on the temperature variable Θ. Firstly, a statement on local existence of classical solutions is derived for arbitrary <em>a</em> > 0, <em>D</em> > 0 as well as 0 < <em>γ</em> ∈ <em>C</em><sup>2</sup>([0, ∞)) and 0 ≤ Γ ∈ <em>C</em><sup>1</sup>([0, ∞)), for functions <span><math><mrow><mi>f</mi><mo>∈</mo><msup><mi>C</mi><mn>2</mn></msup><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>;</mo><msup><mi>R</mi><mi>n</mi></msup><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>F</mi><mo>∈</mo><msup><mi>C</mi><mn>1</mn></msup><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>;</mo><msup><mi>R</mi><mi>n</mi></msup><mo>)</mo></mrow></mrow></math></span> with <span><math><mrow><mi>F</mi><mo>(</mo><mn>0</mn><mo>)</mo><mo>=</mo><mn>0</mn></mrow></math></span>, and for suitably regular initial data of arbitrary size. Secondly, it is seen that under an additional assumption on smallness of <em>a, f</em>′ and <em>F</em>, as well as on the deviation of the initial data from the constant state given by <span><math><mrow><mi>u</mi><mo>=</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mstyle><mi>Θ</mi></mstyle><mo>=</mo><msub><mstyle><mi>Θ</mi></mstyle><mi>★</mi>
{"title":"Describing smooth small-data solutions to a quasilinear hyperbolic-parabolic system by W1,p energy analysis","authors":"Leander Claes , Michael Winkler","doi":"10.1016/j.nonrwa.2025.104580","DOIUrl":"10.1016/j.nonrwa.2025.104580","url":null,"abstract":"<div><div>In bounded <em>n</em>-dimensional domains with <em>n</em> ≥ 1, this manuscript examines an initial-boundary value problem for the system<span><span><span><math><mtable><mtr><mtd><mrow><mo>{</mo><mtable><mtr><mtd><mrow><msub><mi>u</mi><mrow><mi>t</mi><mi>t</mi></mrow></msub><mo>=</mo><mi>∇</mi><mo>·</mo><mrow><mo>(</mo><mi>γ</mi><mrow><mo>(</mo><mstyle><mi>Θ</mi></mstyle><mo>)</mo></mrow><mi>∇</mi><msub><mi>u</mi><mi>t</mi></msub><mo>)</mo></mrow><mo>+</mo><mi>a</mi><mi>∇</mi><mo>·</mo><mrow><mo>(</mo><mi>γ</mi><mrow><mo>(</mo><mstyle><mi>Θ</mi></mstyle><mo>)</mo></mrow><mi>∇</mi><mi>u</mi><mo>)</mo></mrow><mo>+</mo><mi>∇</mi><mo>·</mo><mi>f</mi><mrow><mo>(</mo><mstyle><mi>Θ</mi></mstyle><mo>)</mo></mrow><mo>,</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mstyle><mi>Θ</mi></mstyle><mi>t</mi></msub><mo>=</mo><mi>D</mi><mstyle><mi>Δ</mi></mstyle><mstyle><mi>Θ</mi></mstyle><mo>+</mo><mstyle><mi>Γ</mi></mstyle><mrow><mo>(</mo><mstyle><mi>Θ</mi></mstyle><mo>)</mo></mrow><msup><mrow><mo>|</mo><mi>∇</mi><msub><mi>u</mi><mi>t</mi></msub><mo>|</mo></mrow><mn>2</mn></msup><mo>+</mo><mi>F</mi><mrow><mo>(</mo><mstyle><mi>Θ</mi></mstyle><mo>)</mo></mrow><mo>·</mo><mi>∇</mi><msub><mi>u</mi><mi>t</mi></msub><mo>,</mo></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></math></span></span></span>which in the case <span><math><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow></math></span> and with <em>γ</em> ≡ Γ as well as <em>f</em> ≡ <em>F</em> reduces to the classical model for the evolution of displacement and temperatures in thermoviscoelasticity. Unlike in previous related studies, the focus here is on situations in which besides <em>f</em> and <em>F</em>, also the core ingredients <em>γ</em> and Γ may depend on the temperature variable Θ. Firstly, a statement on local existence of classical solutions is derived for arbitrary <em>a</em> > 0, <em>D</em> > 0 as well as 0 < <em>γ</em> ∈ <em>C</em><sup>2</sup>([0, ∞)) and 0 ≤ Γ ∈ <em>C</em><sup>1</sup>([0, ∞)), for functions <span><math><mrow><mi>f</mi><mo>∈</mo><msup><mi>C</mi><mn>2</mn></msup><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>;</mo><msup><mi>R</mi><mi>n</mi></msup><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>F</mi><mo>∈</mo><msup><mi>C</mi><mn>1</mn></msup><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>;</mo><msup><mi>R</mi><mi>n</mi></msup><mo>)</mo></mrow></mrow></math></span> with <span><math><mrow><mi>F</mi><mo>(</mo><mn>0</mn><mo>)</mo><mo>=</mo><mn>0</mn></mrow></math></span>, and for suitably regular initial data of arbitrary size. Secondly, it is seen that under an additional assumption on smallness of <em>a, f</em>′ and <em>F</em>, as well as on the deviation of the initial data from the constant state given by <span><math><mrow><mi>u</mi><mo>=</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mstyle><mi>Θ</mi></mstyle><mo>=</mo><msub><mstyle><mi>Θ</mi></mstyle><mi>★</mi>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104580"},"PeriodicalIF":1.8,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-01Epub Date: 2025-12-23DOI: 10.1016/j.nonrwa.2025.104573
Rafael Muñoz-Sola
The aim of this paper is to study a model of electromagnetic levitation for a metallic rigid body. The model is constituted by the transient linear model of eddy currents under the hypothesis of axisymmetry, written in terms of a magnetic potential vector, coupled with an ODE which governs the vertical motion of the body. The electromagnetic model is a parabolic-elliptic PDE which parabolicity region is the position occupied by the body, which changes with time. Besides, Lorentz force appears in the RHS of the ODE. Thus, the model exhibits a coupling of geometrical nature. We establish the existence and uniqueness of solution of the coupled problem and we study its maximally defined solution. In particular, we prove that a blow-up of the velocity of the body cannot happen. Our techniques involve: a reformulation of the coupled problem as a causal differential equation, an adaptation of the theory about this kind of equations and a result of locally Lipschitz dependence of the magnetic potential vector with respect to the velocity of the body.
{"title":"Mathematical analysis of a levitation model","authors":"Rafael Muñoz-Sola","doi":"10.1016/j.nonrwa.2025.104573","DOIUrl":"10.1016/j.nonrwa.2025.104573","url":null,"abstract":"<div><div>The aim of this paper is to study a model of electromagnetic levitation for a metallic rigid body. The model is constituted by the transient linear model of eddy currents under the hypothesis of axisymmetry, written in terms of a magnetic potential vector, coupled with an ODE which governs the vertical motion of the body. The electromagnetic model is a parabolic-elliptic PDE which parabolicity region is the position occupied by the body, which changes with time. Besides, Lorentz force appears in the RHS of the ODE. Thus, the model exhibits a coupling of geometrical nature. We establish the existence and uniqueness of solution of the coupled problem and we study its maximally defined solution. In particular, we prove that a blow-up of the velocity of the body cannot happen. Our techniques involve: a reformulation of the coupled problem as a causal differential equation, an adaptation of the theory about this kind of equations and a result of locally Lipschitz dependence of the magnetic potential vector with respect to the velocity of the body.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104573"},"PeriodicalIF":1.8,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-01Epub Date: 2026-01-19DOI: 10.1016/j.nonrwa.2026.104603
José Paulo Carvalho dos Santos , Evandro Monteiro , Nelson Henrique Teixeira Lemes , Ana Claudia Pereira
The focus of this research is an epidemic model that examines the spread of rabies in the bovine population, with the spatial diffusion in the bat population, which serves as the vector population. The study investigates both the well-posedness and qualitative behavior of equilibrium points. The paper establishes the well-posedness of the model through Semigroup theory of sectorial operators and existence results for abstract parabolic differential equations. The research also addresses the definition of the basic reproduction number, , which acts as a threshold index point using linearization theory for reaction-diffusion equations in the disease-free equilibrium point. Additionally, the global asymptotic stability is established through the use of a Lyapunov function and energy estimates.
{"title":"An epidemic model for bovine rabies transmission by bats with spatial diffusion","authors":"José Paulo Carvalho dos Santos , Evandro Monteiro , Nelson Henrique Teixeira Lemes , Ana Claudia Pereira","doi":"10.1016/j.nonrwa.2026.104603","DOIUrl":"10.1016/j.nonrwa.2026.104603","url":null,"abstract":"<div><div>The focus of this research is an epidemic model that examines the spread of rabies in the bovine population, with the spatial diffusion in the bat population, which serves as the vector population. The study investigates both the well-posedness and qualitative behavior of equilibrium points. The paper establishes the well-posedness of the model through Semigroup theory of sectorial operators and existence results for abstract parabolic differential equations. The research also addresses the definition of the basic reproduction number, <span><math><msub><mi>R</mi><mn>0</mn></msub></math></span>, which acts as a threshold index point using linearization theory for reaction-diffusion equations in the disease-free equilibrium point. Additionally, the global asymptotic stability is established through the use of a Lyapunov function and energy estimates.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104603"},"PeriodicalIF":1.8,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146037633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-01Epub Date: 2026-01-31DOI: 10.1016/j.nonrwa.2026.104613
Boubakr Lamouri , Ahmed Boudaoui , Salih Djilali
We investigate a nonlocal SIS epidemic model that incorporates distinct mobility patterns for susceptible and infected individuals, together with a logistic growth. The model includes distinct nonlocal diffusion kernels, denoted by J1(x) and J2(x), which represent different mobility strategies of the susceptible and infected populations, respectively. This formulation enhances the biological realism of the model by allowing greater flexibility in the representation of individual movement behaviors. Consequently, it introduces additional mathematical challenges in the analysis while providing a more accurate modelling for studying the spatial spread of infectious diseases. We establish the well-posedness, positivity, and uniform boundedness of solutions, and prove the existence of a global attractor. The basic reproduction number is derived, and persistence theory is used to show the existence of an endemic steady state when . We further analyze the asymptotic profiles of the endemic steady states under extreme diffusion limits, highlighting the impact of mobility on disease persistence.
{"title":"Effect of diffusion rates on a nonlocal SIS model with distinct dispersal kernels and logistic source","authors":"Boubakr Lamouri , Ahmed Boudaoui , Salih Djilali","doi":"10.1016/j.nonrwa.2026.104613","DOIUrl":"10.1016/j.nonrwa.2026.104613","url":null,"abstract":"<div><div>We investigate a nonlocal SIS epidemic model that incorporates distinct mobility patterns for susceptible and infected individuals, together with a logistic growth. The model includes distinct nonlocal diffusion kernels, denoted by <strong>J</strong><sub>1</sub>(<em>x</em>) and <strong>J</strong><sub>2</sub>(<em>x</em>), which represent different mobility strategies of the susceptible and infected populations, respectively. This formulation enhances the biological realism of the model by allowing greater flexibility in the representation of individual movement behaviors. Consequently, it introduces additional mathematical challenges in the analysis while providing a more accurate modelling for studying the spatial spread of infectious diseases. We establish the well-posedness, positivity, and uniform boundedness of solutions, and prove the existence of a global attractor. The basic reproduction number <span><math><msub><mi>R</mi><mn>0</mn></msub></math></span> is derived, and persistence theory is used to show the existence of an endemic steady state when <span><math><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>></mo><mn>1</mn></mrow></math></span>. We further analyze the asymptotic profiles of the endemic steady states under extreme diffusion limits, highlighting the impact of mobility on disease persistence.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104613"},"PeriodicalIF":1.8,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146188908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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