Applied Mathematics Letters最新文献

{"title":"Bistable traveling waves of a nonlocal reaction–diffusion model with non-monotone birth pulse","authors":"Binxiang Dai,&nbsp;Yaobin Tang","doi":"10.1016/j.aml.2025.109519","DOIUrl":"10.1016/j.aml.2025.109519","url":null,"abstract":"<div><div>This paper considers a nonlocal reaction–diffusion model with a non-monotone birth pulse and a bistable response term. We define two monotone semiflows and, using the comparison argument, obtain the threshold dynamics between persistence and extinction in bounded domain. Moreover, we apply the asymptotic fixed point theorem to show the existence of bistable traveling wave solutions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109519"},"PeriodicalIF":2.9,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143520749","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}

{"title":"About stability of a mathematical model of Glassy-winged Sharpshooter population under Poisson’s jumps","authors":"Leonid Shaikhet","doi":"10.1016/j.aml.2025.109523","DOIUrl":"10.1016/j.aml.2025.109523","url":null,"abstract":"<div><div>The known mathematical model of Glassy-winged Sharpshooter, described by a nonlinear differential equation with delay, is considered under a combination of stochastic perturbations of the type of white noise and Poisson’s jumps. It is assumed that stochastic perturbations are directly proportional to the deviation of the system state from the positive equilibrium. Via the general method of Lyapunov functionals construction two different conditions for stability in probability of the model equilibrium are obtained. Numerical simulations and figures illustrate the obtained results.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109523"},"PeriodicalIF":2.9,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143535240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Uniqueness of weak solutions to one-dimensional doubly degenerate cross-diffusion system","authors":"Xiuqing Chen,&nbsp;Bang Du","doi":"10.1016/j.aml.2025.109521","DOIUrl":"10.1016/j.aml.2025.109521","url":null,"abstract":"<div><div>The uniqueness of global weak solutions to one-dimensional doubly degenerate cross-diffusion system is shown. The equations model the evolution of feeding bacterial populations in a malnourished environment. The key idea of the proof is applying anti-derivative of the sum of weak solutions to the system.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109521"},"PeriodicalIF":2.9,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143529760","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}

{"title":"Sharp-interface limit of the Cahn–Hilliard–Biot equations","authors":"Erlend Storvik,&nbsp;Carina Bringedal","doi":"10.1016/j.aml.2025.109522","DOIUrl":"10.1016/j.aml.2025.109522","url":null,"abstract":"<div><div>In this letter, we derive the sharp-interface limit of the Cahn–Hilliard–Biot equations using formal matched asymptotic expansions. We find that in each sub-domain, the quasi-static Biot equations are obtained with domain-specific material parameters. Moreover, across the interface, material displacement and pore pressure are continuous, while volumetric fluid content and normal stress are balanced. By utilizing the energy of the system, the phase-field potential is shown to be influenced by the curvature, along with contributions from both flow and elasticity at the interface. The normal velocity of the interface is proportional to the jump in normal derivative of the phase-field potential across the interface. Finally, we present a numerical experiment that demonstrates how the location of each phase evolves consistently as the diffuse-interface width parameter becomes smaller; only the width of the diffuse interface changes.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109522"},"PeriodicalIF":2.9,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143526860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamics of non-local lattice systems in ℓ1","authors":"Jiaohui Xu ,&nbsp;Tomás Caraballo ,&nbsp;José Valero","doi":"10.1016/j.aml.2025.109509","DOIUrl":"10.1016/j.aml.2025.109509","url":null,"abstract":"<div><div>In this paper, the well-posedness and asymptotic behavior of a non-local lattice system are analyzed in the space <span><math><msup><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>. In fact, the analysis is carried out in the subspace <span><math><msubsup><mrow><mi>ℓ</mi></mrow><mrow><mo>+</mo></mrow><mrow><mn>1</mn></mrow></msubsup></math></span> formed by the nonnegative elements, remaining open the case of the whole space. The same problem has been analyzed recently in the space <span><math><msup><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> (see Y. Li et al., Communications on Pure and Applied Analysis, 23 (2024), 935-960). However, the latter does not allow us to consider non-local terms which are natural in the modeling of reaction–diffusion problems introduced by M. Chipot in the wide literature published on this problem. With the current analysis, it is possible to investigate these interesting situations.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"165 ","pages":"Article 109509"},"PeriodicalIF":2.9,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510544","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}

{"title":"Localized radial basis function collocation method for long-time simulation of nonlinear transient heat conduction problems","authors":"Yikun Wang ,&nbsp;Xiaohan Jing ,&nbsp;Lin Qiu","doi":"10.1016/j.aml.2025.109525","DOIUrl":"10.1016/j.aml.2025.109525","url":null,"abstract":"<div><div>This paper introduces a hybrid numerical method for simulating two- and three-dimensional nonlinear transient heat conduction problems with temperature-dependent thermal conductivity over extended time intervals. The approach employs the Krylov deferred correction method for temporal discretization, which is particularly effective for dynamic simulations requiring high accuracy. After temporal discretization, the resulting nonlinear equation is solved in the spatial domain using the localized radial basis function collocation method, with its performance further improved by incorporating a newly developed radial basis function. Numerical experiments on two test cases validate the effectiveness and stability of the proposed hybrid method.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"165 ","pages":"Article 109525"},"PeriodicalIF":2.9,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143519811","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}

{"title":"Global solvability in a singular chemotaxis system with logistic source and non-sublinear production","authors":"Xiangdong Zhao,&nbsp;Jiao Wang","doi":"10.1016/j.aml.2025.109511","DOIUrl":"10.1016/j.aml.2025.109511","url":null,"abstract":"<div><div>This paper deals with a singular chemotaxis system with logistic source and non-sublinear production under homogeneous boundary condition: <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>u</mi><mo>−</mo><mi>χ</mi><mo>∇</mo><mi>⋅</mi><mrow><mo>(</mo><mfrac><mrow><mi>u</mi></mrow><mrow><mi>v</mi></mrow></mfrac><mo>∇</mo><mi>v</mi><mo>)</mo></mrow><mo>+</mo><mi>r</mi><mi>u</mi><mo>−</mo><mi>μ</mi><msup><mrow><mi>u</mi></mrow><mrow><mi>k</mi></mrow></msup></mrow></math></span>, <span><math><mrow><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>v</mi><mo>−</mo><mi>v</mi><mo>+</mo><msup><mrow><mi>u</mi></mrow><mrow><mi>β</mi></mrow></msup></mrow></math></span> in a bounded convex domain <span><math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></math></span> with <span><math><mrow><mi>n</mi><mo>≥</mo><mn>1</mn></mrow></math></span>, here <span><math><mrow><mi>χ</mi><mo>,</mo><mi>μ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>, <span><math><mrow><mi>r</mi><mo>∈</mo><mi>R</mi></mrow></math></span>, <span><math><mrow><mi>k</mi><mo>&gt;</mo><mn>1</mn></mrow></math></span> and <span><math><mrow><mi>β</mi><mo>≥</mo><mn>1</mn></mrow></math></span>. It is proved that the system admits a global solution if <span><math><mrow><mi>k</mi><mo>&gt;</mo><mn>2</mn></mrow></math></span> with <span><math><mrow><mi>β</mi><mo>∈</mo><mrow><mo>[</mo><mn>1</mn><mo>,</mo><mi>k</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>, or <span><math><mrow><mi>k</mi><mo>&gt;</mo><mn>1</mn></mrow></math></span> and <span><math><mrow><mi>β</mi><mo>≥</mo><mn>1</mn></mrow></math></span> with <span><math><mrow><mi>χ</mi><mo>≤</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mi>n</mi><msup><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mrow></math></span>. Moreover, the solution is globally bounded for the second case with <span><math><mrow><mi>r</mi><mo>≤</mo><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>β</mi></mrow></mfrac></mrow></math></span>. This means that the logistic source along with non-sublinear production indeed benefits to ensure the global existence-boundedness of classical solution to this chemotaxis system with singular sensitivity.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"165 ","pages":"Article 109511"},"PeriodicalIF":2.9,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511197","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}

{"title":"Bound state with prescribed angular momentum and mass","authors":"Wenbo Wang ,&nbsp;Quanqing Li ,&nbsp;Yuanyang Yu","doi":"10.1016/j.aml.2025.109508","DOIUrl":"10.1016/j.aml.2025.109508","url":null,"abstract":"<div><div>As a continuation of Wang (2024), in the present paper, we consider the following problem in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>V</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>u</mi><mo>=</mo><mi>λ</mi><mrow><mo>(</mo><mo>−</mo><mi>i</mi><msup><mrow><mi>x</mi></mrow><mrow><mo>⊥</mo></mrow></msup><mi>⋅</mi><mo>∇</mo><mi>u</mi><mo>)</mo></mrow><mo>+</mo><mi>μ</mi><mi>u</mi><mo>+</mo><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi></mrow></msup><mi>u</mi><mo>,</mo><mi>u</mi><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>,</mo><mi>ℂ</mi><mo>)</mo></mrow><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mo>∫</mo></mrow><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></msub><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mi>d</mi><mi>x</mi><mo>=</mo><mi>m</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><mi>R</mi><mi>e</mi><msub><mrow><mo>∫</mo></mrow><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></msub><mrow><mo>(</mo><mo>−</mo><mi>i</mi><msup><mrow><mi>x</mi></mrow><mrow><mo>⊥</mo></mrow></msup><mi>⋅</mi><mo>∇</mo><mi>u</mi><mover><mrow><mi>u</mi></mrow><mo>¯</mo></mover><mo>)</mo></mrow><mi>d</mi><mi>x</mi><mo>=</mo><mi>l</mi><mo>∈</mo><mi>R</mi><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>where <span><math><mrow><mi>N</mi><mo>=</mo><mn>2</mn></mrow></math></span> or <span><math><mrow><mi>N</mi><mo>=</mo><mn>3</mn></mrow></math></span>, <span><math><msup><mrow><mi>x</mi></mrow><mrow><mo>⊥</mo></mrow></msup></math></span> is the magnetic potential (see Introduction). When <span><math><mrow><mfrac><mrow><mi>l</mi></mrow><mrow><mi>m</mi></mrow></mfrac><mo>∉</mo><mi>Z</mi></mrow></math></span>, <span><math><mrow><mn>2</mn><mo>&lt;</mo><mi>p</mi><mo>+</mo><mn>2</mn><mo>&lt;</mo><mn>2</mn><mo>+</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mi>N</mi></mrow></mfrac></mrow></math></span>, under suitable assumptions for <span><math><mi>V</mi></math></span>, the existence of bound state is given via a double constrained energy minimization. And the Pohozaev identity is given. <span><math><mi>V</mi></math></span> grows super-quadratically at infinity is needed in our proof.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"165 ","pages":"Article 109508"},"PeriodicalIF":2.9,"publicationDate":"2025-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511196","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}

{"title":"Remarks on Navier–Stokes regularity criteria in Vishik-type spaces","authors":"Fan Wu","doi":"10.1016/j.aml.2025.109506","DOIUrl":"10.1016/j.aml.2025.109506","url":null,"abstract":"<div><div>This note investigates the formation of singularities for the 3D Navier–Stokes equations. By employing a bilinear estimate and a logarithmic interpolation inequality, we derive a new extension criterion based on two vorticity components in Vishik-type spaces, which refines several previously established results concerning Navier–Stokes equations.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"165 ","pages":"Article 109506"},"PeriodicalIF":2.9,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474114","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}

{"title":"Propagating terrace with infinite speed in cooperative systems with multiple types of diffusions","authors":"Biao Liu ,&nbsp;Wan-Tong Li ,&nbsp;Wen-Bing Xu","doi":"10.1016/j.aml.2025.109507","DOIUrl":"10.1016/j.aml.2025.109507","url":null,"abstract":"<div><div>This paper is concerned with the spatial propagation of cooperative systems with general diffusions including multiple types of nonlocal dispersal mechanisms. We show the diversity of long-term behavioral patterns exhibited by different components within these systems, under the assumption that the diffusion operator bring about infinite spreading speed in propagation dynamics. Specifically, we observe that certain components may manifest as propagating terraces with multiple steps, while others exhibit single-front profiles under specific conditions, but it is also possible for all components to display single-front profiles, depending on the selection of coefficients. Furthermore, we prove that the solutions tend to flatten as the spatial propagation has infinite speed.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"165 ","pages":"Article 109507"},"PeriodicalIF":2.9,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474115","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}