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: 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}
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: 2026-02-22DOI: 10.1016/j.cam.2026.117411
Mengnan Li , Shan Zhang , Xiaofei Guan
In this paper, we present an ensemble-based model reduction method to solve random diffusion problems in porous media. The randomness and multiscale pose significant challenges for simulating these problems. To overcome this difficulty, we develop an ensemble-based iterative algorithm by integrating ensemble Monte Carlo (EMC) method with constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM). For random diffusion problems, traditional methods strongly rely on sampling the random space. This necessitates solving the corresponding PDEs for a large number of samples, resulting in high computational costs. To this end, we propose an ensemble method to ensure that all samples share a common stiffness matrix. This significantly improves the computational efficiency. Furthermore, this ensemble method can be combined with LU decomposition or block Krylov subspace iterative methods to further improve computational efficiency. Although the ensemble method avoids solving PDEs multiple times, the high-dimensional challenges posed by the multiscale characteristics remain. Therefore, we employ CEM-GMsFEM to construct an effective reduced-order ensemble model, reducing computational costs. For the proposed ensemble method, we provide a rigorous convergence analysis. A few numerical examples are presented to show the effectiveness of the proposed method.
{"title":"An ensemble-based model reduction method for random diffusion problems in porous media","authors":"Mengnan Li , Shan Zhang , Xiaofei Guan","doi":"10.1016/j.cam.2026.117411","DOIUrl":"10.1016/j.cam.2026.117411","url":null,"abstract":"<div><div>In this paper, we present an ensemble-based model reduction method to solve random diffusion problems in porous media. The randomness and multiscale pose significant challenges for simulating these problems. To overcome this difficulty, we develop an ensemble-based iterative algorithm by integrating ensemble Monte Carlo (EMC) method with constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM). For random diffusion problems, traditional methods strongly rely on sampling the random space. This necessitates solving the corresponding PDEs for a large number of samples, resulting in high computational costs. To this end, we propose an ensemble method to ensure that all samples share a common stiffness matrix. This significantly improves the computational efficiency. Furthermore, this ensemble method can be combined with LU decomposition or block Krylov subspace iterative methods to further improve computational efficiency. Although the ensemble method avoids solving PDEs multiple times, the high-dimensional challenges posed by the multiscale characteristics remain. Therefore, we employ CEM-GMsFEM to construct an effective reduced-order ensemble model, reducing computational costs. For the proposed ensemble method, we provide a rigorous convergence analysis. A few numerical examples are presented to show the effectiveness of the proposed method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117411"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386622","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.2026.117472
Dingyi Ai , Tingsong Du
Herein, we are particularly intrigued by exploring Radau-type inequalities that emerge from multiplicative Katugampola fractional integrals. To that end, we commence by introducing the concept of such integrals. And several analytical properties, such as boundedness, continuity, commutativity, semigroup property, and others, are examined for the freshly introduced operators. Following this, we derive an identity pertinent to multiplicative Katugampola fractional integrals, which forms the basis for establishing a series of Radau-type inequalities in our investigation. These inequalities are derived under the condition that either the function f* is multiplicatively convex or the function (ln ∘f*)q is convex for q > 1, with a specific focus on the scenario where 0 < q ≤ 1. To deepen the readers’ profound comprehension of the acquired results, we present illustrative examples along with accompanying graphs, which confirm the correctness of the derived inequalities. Finally, we showcase the applicability of these inequalities presented here in various contexts, including multiplicative differential equations, quadrature formulas, and special means.
{"title":"Radau-type inequalities from multiplicative Katugampola fractional integrals theoretical point of view","authors":"Dingyi Ai , Tingsong Du","doi":"10.1016/j.cam.2026.117472","DOIUrl":"10.1016/j.cam.2026.117472","url":null,"abstract":"<div><div>Herein, we are particularly intrigued by exploring Radau-type inequalities that emerge from multiplicative Katugampola fractional integrals. To that end, we commence by introducing the concept of such integrals. And several analytical properties, such as boundedness, continuity, commutativity, semigroup property, and others, are examined for the freshly introduced operators. Following this, we derive an identity pertinent to multiplicative Katugampola fractional integrals, which forms the basis for establishing a series of Radau-type inequalities in our investigation. These inequalities are derived under the condition that either the function <em>f</em>* is multiplicatively convex or the function (ln ∘<em>f</em>*)<sup><em>q</em></sup> is convex for <em>q</em> > 1, with a specific focus on the scenario where 0 < <em>q</em> ≤ 1. To deepen the readers’ profound comprehension of the acquired results, we present illustrative examples along with accompanying graphs, which confirm the correctness of the derived inequalities. Finally, we showcase the applicability of these inequalities presented here in various contexts, including multiplicative differential equations, quadrature formulas, and special means.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117472"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386626","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: 2026-02-24DOI: 10.1016/j.cam.2026.117487
Gonglin Yuan , Yingjie Zhou , Fanhua Shang , Zhijin Ge , Zhongzhou Jin
It is known that the limited memory BFGS (L-BFGS) method is an important method for solving nonlinear optimization. For stochastic optimization problems, especially for nonconvex functions, it is difficult to preserve Bk≻0 (the inverse of the Hessian matrix) for all k due to the noise incurred by estimating the gradient and the nonconvexity of the functions. In this paper, we propose a novel modified stochastic L-BFGS algorithm (MSLBFGS) for solving nonconvex optimization, where the positive definiteness of the designed matrix Bk is automatically maintained. We establish the convergence property of the proposed MSLBFGS algorithm. In the worst-case scenario, we output , and prove that the number of the stochastic first-order oracle calls of the proposed algorithm with a diminishing step length is due to β ∈ (0.5, 1). Moreover, we also present a new modified stochastic L-BFGS algorithm that incorporates the variance reduction technique. Numerical experiments conducted on nonconvex support vector machine problems and nonconvex empirical risk minimization problems validate the effectiveness of the proposed algorithms, showing their advantages over existing methods.
{"title":"Stochastic limited memory BFGS algorithms for solving nonconvex support vector machine problems and nonconvex risk minimization program","authors":"Gonglin Yuan , Yingjie Zhou , Fanhua Shang , Zhijin Ge , Zhongzhou Jin","doi":"10.1016/j.cam.2026.117487","DOIUrl":"10.1016/j.cam.2026.117487","url":null,"abstract":"<div><div>It is known that the limited memory BFGS (L-BFGS) method is an important method for solving nonlinear optimization. For stochastic optimization problems, especially for nonconvex functions, it is difficult to preserve <em>B<sub>k</sub></em>≻0 (the inverse of the Hessian matrix) for all <em>k</em> due to the noise incurred by estimating the gradient and the nonconvexity of the functions. In this paper, we propose a novel modified stochastic L-BFGS algorithm (MSLBFGS) for solving nonconvex optimization, where the positive definiteness of the designed matrix <em>B<sub>k</sub></em> is automatically maintained. We establish the convergence property of the proposed MSLBFGS algorithm. In the worst-case scenario, we output <span><math><mrow><mfrac><mn>1</mn><mi>N</mi></mfrac><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></msubsup><mrow><mi>E</mi><mo>[</mo><mo>∥</mo><mi>∇</mi><mi>f</mi></mrow><mrow><mo>(</mo><msub><mi>x</mi><mi>k</mi></msub><mo>)</mo></mrow><mrow><msup><mo>∥</mo><mn>2</mn></msup><mo>]</mo></mrow><mo><</mo><mrow><mi>ε</mi></mrow></mrow></math></span>, and prove that the number of the stochastic first-order oracle calls of the proposed algorithm with a diminishing step length is <span><math><mrow><mi>O</mi><mo>(</mo><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>−</mo><mi>β</mi></mrow></mfrac></mrow></msup><mo>)</mo></mrow></math></span> due to <em>β</em> ∈ (0.5, 1). Moreover, we also present a new modified stochastic L-BFGS algorithm that incorporates the variance reduction technique. Numerical experiments conducted on nonconvex support vector machine problems and nonconvex empirical risk minimization problems validate the effectiveness of the proposed algorithms, showing their advantages over existing methods.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117487"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386631","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}
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