Applied Mathematics Letters最新文献

{"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}

{"title":"Traveling wave fronts for a discrete Nicholson’s blowflies model with two delays","authors":"Ruiwen Wu ,&nbsp;Zhiting Xu","doi":"10.1016/j.aml.2025.109505","DOIUrl":"10.1016/j.aml.2025.109505","url":null,"abstract":"<div><div>This paper is devoted to investigate a discrete Nicholson’s blowflies model with two delays. We construct some novel upper and lower solutions for the wave equation and then show the equation admits the traveling wave fronts connecting two equilibria of the associated spatially homogeneous system. And also, we obtain the non-existence for traveling waves of the model.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"165 ","pages":"Article 109505"},"PeriodicalIF":2.9,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143471144","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":"Minimal wave speed of competitive diffusive systems with time delays","authors":"Yanli Huang,&nbsp;Guo Lin","doi":"10.1016/j.aml.2025.109504","DOIUrl":"10.1016/j.aml.2025.109504","url":null,"abstract":"<div><div>This paper is concerned with the minimal wave speed of exclusion traveling wave solutions in a delayed competitive systems. Because of the intraspecific delays, the system cannot generate monotone semiflows. We give the minimal wave speed by combining different recipes. Here, the minimal wave speed is linearly determinate.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"165 ","pages":"Article 109504"},"PeriodicalIF":2.9,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143465250","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":"Optimal-order balanced-norm error estimate of the local discontinuous Galerkin method with alternating numerical flux for singularly perturbed reaction–diffusion problems","authors":"Juan Kang,&nbsp;Yao Cheng","doi":"10.1016/j.aml.2025.109503","DOIUrl":"10.1016/j.aml.2025.109503","url":null,"abstract":"<div><div>Balanced-norm error bounds have been established in Cheng et al. (2022) for the local discontinuous Galerkin (LDG) method using alternating numerical flux on Shishkin-type meshes. However, the convergence rate is shown to be one-half order lower than the numerical results in the general case. This paper seeks to fill up this gap by introducing a new composite projector in the error analysis. We achieve an optimal-order error estimate in the balanced-norm for the LDG method on both Shishkin-type and Bakhvalov-type meshes, uniformly in the small perturbation parameter.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"165 ","pages":"Article 109503"},"PeriodicalIF":2.9,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143454989","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":"On a two-component Camassa–Holm equation","authors":"Zixin Zhang,&nbsp;Q.P. Liu","doi":"10.1016/j.aml.2025.109502","DOIUrl":"10.1016/j.aml.2025.109502","url":null,"abstract":"<div><div>A two-component generalization of the Camassa–Holm equation and its reduction proposed recently by Xue, Du and Geng [Appl. Math. Lett. <strong>146</strong> (2023) 108795] are studied. For this two-component equation, its missing bi-Hamiltonian structure is constructed and a Miura transformation is introduced so that it may be regarded as a modification of the very first two-component Camassa–Holm equation. Using a proper reciprocal transformation, a particular reduction of this two-component equation, which admits <span><math><mi>N</mi></math></span>-peakon solution, is shown to be a flow of the integrable hierarchy related to the celebrated Burgers equation.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"165 ","pages":"Article 109502"},"PeriodicalIF":2.9,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143454988","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}