Pub Date : 2026-02-01Epub Date: 2025-10-29DOI: 10.1016/j.aml.2025.109802
Mingxi Li, Qian Zhang
We study the Cauchy problem for the 3D axisymmetric chemotaxis-Navier–Stokes equations with nonlinear diffusion . Leveraging the axisymmetric non-swirl flow structure, we extend the range of to and prove the global existence of weak solutions for this model. Besides we extend the global result from bounded domain (Winkler, 2015) to the entire spaces.
{"title":"On the global existence of weak solution for the 3D axisymmetric chemotaxis-Navier–Stokes equations with nonlinear diffusion","authors":"Mingxi Li, Qian Zhang","doi":"10.1016/j.aml.2025.109802","DOIUrl":"10.1016/j.aml.2025.109802","url":null,"abstract":"<div><div>We study the Cauchy problem for the 3D axisymmetric chemotaxis-Navier–Stokes equations with nonlinear diffusion <span><math><mrow><mi>Δ</mi><msup><mrow><mi>n</mi></mrow><mrow><mi>m</mi></mrow></msup></mrow></math></span>. Leveraging the axisymmetric non-swirl flow structure, we extend the range of <span><math><mi>m</mi></math></span> to <span><math><mrow><mo>(</mo><mfrac><mrow><mn>7</mn></mrow><mrow><mn>6</mn></mrow></mfrac><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></math></span> and prove the global existence of weak solutions for this model. Besides we extend the global result from bounded domain (Winkler, 2015) to the entire spaces.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109802"},"PeriodicalIF":2.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145382495","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 : 2026-02-01Epub Date: 2025-10-11DOI: 10.1016/j.aml.2025.109788
Hui Kang , Tianfang Wang , Wen Zhang
In this paper, we investigate a class of asymptotically quadratic Dirac–Bopp–Podolsky system in relativistic quantum electrodynamics. As we know that the Dirac operator is unbounded from below and above, then the associated energy functional is strongly indefinite. Applying the multiple critical point theorem of strongly indefinite functionals and concentration compactness arguments, we establish the existence and multiplicity result of nontrivial solutions.
{"title":"Existence and multiplicity of solutions for a class of nonlinear Dirac–Bopp–Podolsky system","authors":"Hui Kang , Tianfang Wang , Wen Zhang","doi":"10.1016/j.aml.2025.109788","DOIUrl":"10.1016/j.aml.2025.109788","url":null,"abstract":"<div><div>In this paper, we investigate a class of asymptotically quadratic Dirac–Bopp–Podolsky system in relativistic quantum electrodynamics. As we know that the Dirac operator is unbounded from below and above, then the associated energy functional is strongly indefinite. Applying the multiple critical point theorem of strongly indefinite functionals and concentration compactness arguments, we establish the existence and multiplicity result of nontrivial solutions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109788"},"PeriodicalIF":2.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145320419","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 : 2026-02-01Epub Date: 2025-10-09DOI: 10.1016/j.aml.2025.109782
Ying Chao , Jinqiao Duan , Pingyuan Wei
We investigate the exit problem from the domain of attraction of a stable state in kinetic Langevin systems with nongradient perturbations. Using Freidlin–Wentzell large deviation theory, we analyze the most probable escape paths and, through a Hamiltonian formulation combined with Melnikov theory, establish conditions under which the optimal escape path persists as a heteroclinic orbit in the perturbed system. Our results demonstrate that, in the presence of nongradient perturbations, the most probable escape path differs from the time-reversed heteroclinic orbit at leading order in the intensity of the autonomous perturbation. These theoretical findings are corroborated by a numerical example.
{"title":"Most probable escape paths in perturbed kinetic Langevin systems","authors":"Ying Chao , Jinqiao Duan , Pingyuan Wei","doi":"10.1016/j.aml.2025.109782","DOIUrl":"10.1016/j.aml.2025.109782","url":null,"abstract":"<div><div>We investigate the exit problem from the domain of attraction of a stable state in kinetic Langevin systems with nongradient perturbations. Using Freidlin–Wentzell large deviation theory, we analyze the most probable escape paths and, through a Hamiltonian formulation combined with Melnikov theory, establish conditions under which the optimal escape path persists as a heteroclinic orbit in the perturbed system. Our results demonstrate that, in the presence of nongradient perturbations, the most probable escape path differs from the time-reversed heteroclinic orbit at leading order in the intensity of the autonomous perturbation. These theoretical findings are corroborated by a numerical example.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109782"},"PeriodicalIF":2.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145268035","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 : 2026-02-01Epub Date: 2025-10-10DOI: 10.1016/j.aml.2025.109787
Jian Liu
This paper establishes the existence and uniqueness of weak solutions for a class of double-degenerate singular elliptic equations involving -Laplacian operator with weight functions and and a gradient-dependent nonlinearity. We introduce a novel weighted boundedness condition based on to handle singular coefficients and relax regularity requirements. To the best of our knowledge, such conditions have not been previously addressed in the literature. Working in the weighted Sobolev space , we prove the associated operator is bounded, coercive, semicontinuous, and strictly monotone. Applying the Minty–Browder theorem, we obtain an explicit parameter range for ensuring a unique weak solution.
{"title":"Degenerate (p,r)-Laplacian elliptic equations under weighted boundedness conditions","authors":"Jian Liu","doi":"10.1016/j.aml.2025.109787","DOIUrl":"10.1016/j.aml.2025.109787","url":null,"abstract":"<div><div>This paper establishes the existence and uniqueness of weak solutions for a class of double-degenerate singular elliptic equations involving <span><math><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>r</mi><mo>)</mo></mrow></math></span>-Laplacian operator with weight functions <span><math><mrow><mi>ω</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>ϑ</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> and a gradient-dependent nonlinearity. We introduce a novel weighted boundedness condition based on <span><math><mrow><mi>ω</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> to handle singular coefficients and relax regularity requirements. To the best of our knowledge, such conditions have not been previously addressed in the literature. Working in the weighted Sobolev space <span><math><mrow><msubsup><mrow><mi>W</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn><mo>,</mo><mi>p</mi></mrow></msubsup><mrow><mo>(</mo><mi>ω</mi><mo>,</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span>, we prove the associated operator is bounded, coercive, semicontinuous, and strictly monotone. Applying the Minty–Browder theorem, we obtain an explicit parameter range for <span><math><mi>λ</mi></math></span> ensuring a unique weak solution.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109787"},"PeriodicalIF":2.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145268037","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 : 2026-02-01Epub Date: 2025-09-14DOI: 10.1016/j.aml.2025.109757
Wei Wang , Guoxiao Wu , Xiaoting Fan
Pyroptosis is a primary cause of viral infection of CD4+ T cells. The canonical inflammatory signaling pathway depends on the activation of Pattern Recognition Receptors (PRR). PRR (NLRP3 inflammasome, etc.) activation is a critical step that mediates subsequent Gasdermin D (GSDMD) protein activation and cellular pyroptosis. In this article, we develop a novel model of viral dynamics mediated by PRR. We first prove the existence of equilibria, and define the basic reproduction number . Then the global stability of equilibria is investigated by establishing the appropriate Lyapunov functions.
焦亡是病毒感染CD4+ T细胞的主要原因。典型的炎症信号通路依赖于模式识别受体（PRR）的激活。PRR （NLRP3炎性小体等）的激活是介导后续Gasdermin D （GSDMD）蛋白激活和细胞焦亡的关键步骤。在本文中，我们建立了一个由PRR介导的病毒动力学的新模型。首先证明了均衡的存在性，并定义了基本繁殖数R0。然后通过建立适当的Lyapunov函数来研究平衡点的全局稳定性。
{"title":"Global dynamics of a novel viral infection model mediated by pattern recognition receptors","authors":"Wei Wang , Guoxiao Wu , Xiaoting Fan","doi":"10.1016/j.aml.2025.109757","DOIUrl":"10.1016/j.aml.2025.109757","url":null,"abstract":"<div><div>Pyroptosis is a primary cause of viral infection of CD4+ T cells. The canonical inflammatory signaling pathway depends on the activation of Pattern Recognition Receptors (PRR). PRR (NLRP3 inflammasome, etc.) activation is a critical step that mediates subsequent Gasdermin D (GSDMD) protein activation and cellular pyroptosis. In this article, we develop a novel model of viral dynamics mediated by PRR. We first prove the existence of equilibria, and define the basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>. Then the global stability of equilibria is investigated by establishing the appropriate Lyapunov functions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109757"},"PeriodicalIF":2.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097044","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 : 2026-02-01Epub Date: 2025-09-19DOI: 10.1016/j.aml.2025.109768
Linlin Gui, Yufeng Zhang
Manakov and Santini, etc., have solved inverse scattering problem for dispersionless integrable partial differential equations (PDEs), and used these to construct the formal solutions for integrable equations. In this paper, we derive a new equation from a pair of two-dimensional vector fields, termed the generalized r-th dispersionless Harry Dym (g-rdDym) equation, which reduces to the standard (2+1)-dimensional r-th dispersionless Harry Dym (rdDym) equation. Then we construct large behaviour of formal solution of Cauchy problem by applying associated Riemann-Hilbert (RH) inverse problem, and describe a new class of particular solutions via the exponential functions. This paper investigates not only the rdDym equation, but also its corresponding generalized equation, i.e. the g-rdDym equation.
{"title":"The large t behaviour of solutions for a new generalized r-th dispersionless Harry Dym equation","authors":"Linlin Gui, Yufeng Zhang","doi":"10.1016/j.aml.2025.109768","DOIUrl":"10.1016/j.aml.2025.109768","url":null,"abstract":"<div><div>Manakov and Santini, etc., have solved inverse scattering problem for dispersionless integrable partial differential equations (PDEs), and used these to construct the formal solutions for integrable equations. In this paper, we derive a new equation from a pair of two-dimensional vector fields, termed the generalized r-th dispersionless Harry Dym (g-rdDym) equation, which reduces to the standard (2+1)-dimensional r-th dispersionless Harry Dym (rdDym) equation. Then we construct large <span><math><mi>t</mi></math></span> behaviour of formal solution of Cauchy problem by applying associated Riemann-Hilbert (RH) inverse problem, and describe a new class of particular solutions via the exponential functions. This paper investigates not only the rdDym equation, but also its corresponding generalized equation, i.e. the g-rdDym equation.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109768"},"PeriodicalIF":2.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097041","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 : 2026-02-01Epub Date: 2025-09-17DOI: 10.1016/j.aml.2025.109762
Yarong Xia , Wenjie Huang , Ruoxia Yao
This paper mainly studies the interaction structures of lump wave and other types of localized wave for (2+ 1)-dimensional Sawada–Kotera-like (SK-Like) equation. Firstly, the -soliton solutions are constructed via the Hirota bilinear method. Subsequently, using the long-wave limit method, we derive several distinct hybrid solutions which include lump-line waves, lump-breather waves, and hybrid solution among lump, line and breather waves. At the same time, we discuss that the lump wave neither collides with line waves or breather waves nor always lies on them under the conditions and . In addition, based on the mixed solutions obtained above, by leveraging the velocity resonance mechanism, we construct the soliton molecular bound states among lump wave, line wave, and breather wave. Furthermore, through numerical simulation, vivid pictures of the superposition of lump wave and other nonlinear waves are presented.
{"title":"Interaction structures of (2+1)-dimensional Sawada–Kotera-like equation","authors":"Yarong Xia , Wenjie Huang , Ruoxia Yao","doi":"10.1016/j.aml.2025.109762","DOIUrl":"10.1016/j.aml.2025.109762","url":null,"abstract":"<div><div>This paper mainly studies the interaction structures of lump wave and other types of localized wave for (2+ 1)-dimensional Sawada–Kotera-like (SK-Like) equation. Firstly, the <span><math><mi>N</mi></math></span>-soliton solutions are constructed via the Hirota bilinear method. Subsequently, using the long-wave limit method, we derive several distinct hybrid solutions which include lump-line waves, lump-breather waves, and hybrid solution among lump, line and breather waves. At the same time, we discuss that the lump wave neither collides with line waves or breather waves nor always lies on them under the conditions <span><math><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>=</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>=</mo><mn>0</mn></mrow></math></span>. In addition, based on the mixed solutions obtained above, by leveraging the velocity resonance mechanism, we construct the soliton molecular bound states among lump wave, line wave, and breather wave. Furthermore, through numerical simulation, vivid pictures of the superposition of lump wave and other nonlinear waves are presented.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109762"},"PeriodicalIF":2.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145109586","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 : 2026-02-01Epub Date: 2025-09-29DOI: 10.1016/j.aml.2025.109772
Dongxue Yan , Xinyu Bai , Yu Cao
Using semigroup theories and spectral analysis methods, this paper shows that the solutions of a Daphnia population model with size structure and delayed birth process exhibit asynchronous exponential growth under some conditions.
{"title":"Asynchronous exponential growth for a size-structured population model of Daphnia with delayed birth process","authors":"Dongxue Yan , Xinyu Bai , Yu Cao","doi":"10.1016/j.aml.2025.109772","DOIUrl":"10.1016/j.aml.2025.109772","url":null,"abstract":"<div><div>Using semigroup theories and spectral analysis methods, this paper shows that the solutions of a Daphnia population model with size structure and delayed birth process exhibit asynchronous exponential growth under some conditions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109772"},"PeriodicalIF":2.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220887","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}
A model order reduction method based on shifted Legendre polynomials for solving convection–diffusion equations with variable coefficients is presented in this paper. The ordinary differential system of the convection–diffusion equation is obtained by finite element discretization procedure. Then, approximating the system state via shifted Legendre polynomials, the reduced-order system is produced, which can be solved efficiently to obtain the numerical solution. Error analysis is presented, and numerical examples are used to verify the feasibility of the presented method.
{"title":"Legendre-based model order reduction method for solving convection–diffusion equations with variable coefficients","authors":"Zhiyuan Xing , Yanpeng Li , Xiufang Feng , Yaolin Jiang","doi":"10.1016/j.aml.2025.109773","DOIUrl":"10.1016/j.aml.2025.109773","url":null,"abstract":"<div><div>A model order reduction method based on shifted Legendre polynomials for solving convection–diffusion equations with variable coefficients is presented in this paper. The ordinary differential system of the convection–diffusion equation is obtained by finite element discretization procedure. Then, approximating the system state via shifted Legendre polynomials, the reduced-order system is produced, which can be solved efficiently to obtain the numerical solution. Error analysis is presented, and numerical examples are used to verify the feasibility of the presented method.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109773"},"PeriodicalIF":2.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220888","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 : 2026-02-01Epub Date: 2025-10-21DOI: 10.1016/j.aml.2025.109794
F.Z. Geng , X.Y. Wu
As is known, it is perceived as a difficult problem to obtain an effective approximate solution to boundary value problems (BVPs) with highly oscillatory solutions. Traditional reproducing kernel methods (RKMs) are not effective for highly oscillatory BVPs although the RKM is a useful approach to approximation theory. The aim of the letter is to propose a novel class of RKMs to solve highly oscillatory second-order BVPs. To this end, we begin with the variation-of-constants formula (VCF). We then derive RKMs for highly oscillatory BVPs. Our simulations confirm the high accuracy of the introduced techniques.
{"title":"Numerical algorithms using reproducing kernels for oscillatory boundary value problems","authors":"F.Z. Geng , X.Y. Wu","doi":"10.1016/j.aml.2025.109794","DOIUrl":"10.1016/j.aml.2025.109794","url":null,"abstract":"<div><div>As is known, it is perceived as a difficult problem to obtain an effective approximate solution to boundary value problems (BVPs) with highly oscillatory solutions. Traditional reproducing kernel methods (RKMs) are not effective for highly oscillatory BVPs although the RKM is a useful approach to approximation theory. The aim of the letter is to propose a novel class of RKMs to solve highly oscillatory second-order BVPs. To this end, we begin with the variation-of-constants formula (VCF). We then derive RKMs for highly oscillatory BVPs. Our simulations confirm the high accuracy of the introduced techniques.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109794"},"PeriodicalIF":2.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145362318","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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