Applied Mathematics Letters最新文献

{"title":"A note on Turing–Hopf bifurcation in a diffusive Leslie–Gower model with weak Allee effect on prey and fear effect on predator","authors":"Wenjie Li ,&nbsp;Letian Zhang ,&nbsp;Jinde Cao","doi":"10.1016/j.aml.2025.109741","DOIUrl":"10.1016/j.aml.2025.109741","url":null,"abstract":"<div><div>In this paper, we investigate the dynamics of a diffusive Leslie–Gower model incorporating a weak Allee effect on prey and a fear effect on predators. First, we derive the relevant characteristic equations. Subsequently, we analyze the existence of Turing Hopf bifurcation–phenomena that characterize the emergence of spatial patterns and temporal oscillations driven by diffusion and population dynamics, respectively. Finally, we perform numerical simulations to validate our theoretical results and further illustrate the model dynamics with both weak Allee and predator fear effects.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"172 ","pages":"Article 109741"},"PeriodicalIF":2.8,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144988391","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":"A note on the reliability of goal-oriented error estimates for Galerkin finite element methods with nonlinear functionals","authors":"Brian N. Granzow ,&nbsp;Stephen D. Bond ,&nbsp;D. Thomas Seidl ,&nbsp;Bernhard Endtmayer","doi":"10.1016/j.aml.2025.109742","DOIUrl":"10.1016/j.aml.2025.109742","url":null,"abstract":"<div><div>We consider estimating the discretization error in a nonlinear functional <span><math><mrow><mi>J</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow></mrow></math></span> in the setting of an abstract variational problem: find <span><math><mrow><mi>u</mi><mo>∈</mo><mi>V</mi></mrow></math></span> such that <span><math><mrow><mi>B</mi><mrow><mo>(</mo><mi>u</mi><mo>,</mo><mi>φ</mi><mo>)</mo></mrow><mo>=</mo><mi>L</mi><mrow><mo>(</mo><mi>φ</mi><mo>)</mo></mrow><mspace></mspace><mo>∀</mo><mi>φ</mi><mo>∈</mo><mi>V</mi></mrow></math></span>, as approximated by a Galerkin finite element method. Here, <span><math><mi>V</mi></math></span> is a Hilbert space, <span><math><mrow><mi>B</mi><mrow><mo>(</mo><mi>⋅</mi><mo>,</mo><mi>⋅</mi><mo>)</mo></mrow></mrow></math></span> is a bilinear form, and <span><math><mrow><mi>L</mi><mrow><mo>(</mo><mi>⋅</mi><mo>)</mo></mrow></mrow></math></span> is a linear functional. We consider well-known error estimates <span><math><mi>η</mi></math></span> of the form <span><math><mrow><mi>J</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>−</mo><mi>J</mi><mrow><mo>(</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>h</mi></mrow></msub><mo>)</mo></mrow><mo>≈</mo><mi>η</mi><mo>=</mo><mi>L</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>−</mo><mi>B</mi><mrow><mo>(</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>h</mi></mrow></msub><mo>,</mo><mi>z</mi><mo>)</mo></mrow></mrow></math></span>, where <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>h</mi></mrow></msub></math></span> denotes a finite element approximation to <span><math><mi>u</mi></math></span>, and <span><math><mi>z</mi></math></span> denotes the solution to an auxiliary adjoint variational problem. We show that there exist nonlinear functionals for which error estimates of this form are not reliable, even in the presence of an exact adjoint solution <span><math><mi>z</mi></math></span>. An estimate <span><math><mi>η</mi></math></span> is said to be reliable if there exists a constant <span><math><mrow><mi>C</mi><mo>∈</mo><msub><mrow><mi>R</mi></mrow><mrow><mo>&gt;</mo><mn>0</mn></mrow></msub></mrow></math></span> independent of <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>h</mi></mrow></msub></math></span> such that <span><math><mrow><mrow><mo>|</mo><mi>J</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>−</mo><mi>J</mi><mrow><mo>(</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>h</mi></mrow></msub><mo>)</mo></mrow><mo>|</mo></mrow><mo>≤</mo><mi>C</mi><mrow><mo>|</mo><mi>η</mi><mo>|</mo></mrow></mrow></math></span>. We present several example pairs of bilinear forms and nonlinear functionals where reliability of <span><math><mi>η</mi></math></span> is not achieved.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"172 ","pages":"Article 109742"},"PeriodicalIF":2.8,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144931721","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":"A Crank–Nicolson ultra-weak discontinuous Galerkin method for solving a unsteady singularly perturbed problem with a shift in space","authors":"Yige Liao ,&nbsp;Li-Bin Liu ,&nbsp;Xianbing Luo ,&nbsp;Guangqing Long","doi":"10.1016/j.aml.2025.109736","DOIUrl":"10.1016/j.aml.2025.109736","url":null,"abstract":"<div><div>In this paper, a unsteady singularly perturbed problem (SPP) with a shift in space is studied. The problem is discretized by a ultra-weak discontinuous Galerkin (UWDG) method in space on the Bakhvalov-type (B-type) mesh and by Crank–Nicolson (CN) scheme in time. Through carefully designing numerical fluxes and penalty terms, we rigorously establish the coercivity of the bilinear form associated with the UWDG scheme. Furthermore, based on the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-projection and careful error estimate for Ritz projection, we derive optimal-order convergence estimates. Numerical experiments verify the effectiveness of the method.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"172 ","pages":"Article 109736"},"PeriodicalIF":2.8,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144925290","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":"Homoclinic solutions for a difference equation with the mean curvature operator and periodic coefficients","authors":"Xiaoguang Li ,&nbsp;Zhan Zhou","doi":"10.1016/j.aml.2025.109737","DOIUrl":"10.1016/j.aml.2025.109737","url":null,"abstract":"<div><div>We establish the existence of nontrivial homoclinic solutions for a class of difference equation with the mean curvature operator and periodic potentials via variational methods. Specifically, a novel approach inspired by the <em>vanishing</em> in the <em>concentration–compactness principle</em> is employed to prove the boundedness of Cerami sequences. Finally, we investigate the strict monotonicity and sign-definiteness of the obtained homoclinic solution, which have rarely been discussed.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"172 ","pages":"Article 109737"},"PeriodicalIF":2.8,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144931718","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":"Novel exponential-weighted integral inequality for exponential stability analysis of time-varying delay systems","authors":"Nuo Cheng ,&nbsp;Wei Wang ,&nbsp;Hong-Bing Zeng ,&nbsp;Xinge Liu ,&nbsp;Xian-Ming Zhang","doi":"10.1016/j.aml.2025.109730","DOIUrl":"10.1016/j.aml.2025.109730","url":null,"abstract":"<div><div>This paper investigates the exponential stability of systems with time-varying delays. A novel exponential-weighted integral inequality is developed from the extension of the second-order Bessel–Legendre inequality by introducing suitable coefficients into orthogonal polynomials, which leverages the monotonic property of certain integral ratios derived from orthogonal polynomials. This inequality enables the direct estimation of exponential-weighted integrals with varying limits, without requiring the additional conservative bounding commonly used in existing literature. Utilizing the proposed inequality, two exponential stability criteria are derived, corresponding to two different cases of time-varying delays. Simulations based on two well-studied examples demonstrate the effectiveness of the proposed approach.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"172 ","pages":"Article 109730"},"PeriodicalIF":2.8,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144931719","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 boundedness in a three-species system with indirect prey-taxis","authors":"Qigang Deng,&nbsp;Ali Rehman,&nbsp;Ranchao Wu","doi":"10.1016/j.aml.2025.109738","DOIUrl":"10.1016/j.aml.2025.109738","url":null,"abstract":"<div><div>It is showed that a fully parabolic three-species predator–prey model with indirect prey-taxis in a bounded domain has a globally bounded classical solution, which means the solution will not blow up. The results extend the previous ones in Zheng and Wan (2025). In the high-dimensional setting, conditions on parameters are further relaxed.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"172 ","pages":"Article 109738"},"PeriodicalIF":2.8,"publicationDate":"2025-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144921311","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":"Oscillation theorems for linear Hamiltonian systems with nonlinear dependence on the spectral parameter and separated boundary conditions","authors":"Julia Elyseeva,&nbsp;Natalia Rogozina","doi":"10.1016/j.aml.2025.109740","DOIUrl":"10.1016/j.aml.2025.109740","url":null,"abstract":"<div><div>In this paper, we consider linear Hamiltonian differential systems which depend in general nonlinearly on the spectral parameter and with separated boundary conditions. In our consideration we do not impose any controllability and strict normality assumptions and omit the Legendre condition for the Hamiltonian. The main results generalize our previous investigations for the Hamiltonian spectral problems with Dirichlet boundary conditions. We prove the local and global oscillation theorems relating the number of left finite eigenvalues of the problem in the given interval with the values of the oscillation numbers at the end points of this interval.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109740"},"PeriodicalIF":2.8,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145005415","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 the mathematical structure and solvability of certain Hilbert space optimization problems in data-driven elasticity","authors":"Cristian G. Gebhardt ,&nbsp;Marc C. Steinbach","doi":"10.1016/j.aml.2025.109739","DOIUrl":"10.1016/j.aml.2025.109739","url":null,"abstract":"<div><div>In this theoretical study, we analyze the structure and solvability of data-driven elasticity problems in one spatial dimension. In contrast to Conti, Müller, Ortiz (2018, 2020), who develop an extensive, highly abstract theory for mixed Dirichlet–Neumann problems in arbitrary dimension, our setting provides a direct understanding of the problem structure and of the key issue of existence of minimizers in Hilbert space on a basic technical level. For Dirichlet problems with low regularity, we derive a reduced problem defined on orthogonal subspaces, we give explicit representations of all relevant spaces and operators, and we exploit the orthogonal decomposition to prove solvability for several standard cases and under certain symmetries. For mixed Dirichlet–Neumann problems, we prove universal solvability. In addition, we address the issue of thermomechanical consistency.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"172 ","pages":"Article 109739"},"PeriodicalIF":2.8,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144925289","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":"Space–time generalized finite difference scheme for three-dimensional unsteady nonlinear convection–diffusion–reaction equation","authors":"Fan Zhang,&nbsp;Po-Wei Li,&nbsp;Kexin Yi","doi":"10.1016/j.aml.2025.109722","DOIUrl":"10.1016/j.aml.2025.109722","url":null,"abstract":"<div><div>This paper develops a space–time generalized finite difference method (ST-GFDM), integrated with a time-marching framework and the Levenberg–Marquardt algorithm (LMA), to address three-dimensional unsteady nonlinear convection–diffusion–reaction equations. The ST-GFDM, as a meshless approach combined with a space–time formulation, approximates spatial and temporal derivatives by solving a local least-squares system derived from Taylor series expansion within the ST domain. Through this formulation, the governing PDEs are converted into a nonlinear algebraic system, efficiently resolved via a two-step LMA iteration. The time-marching mechanism incrementally propagates the ST computational domain forward along the temporal axis, which significantly reduces memory usage and enhances performance in long-duration simulations. The unified treatment of time and space discretization further improves numerical robustness, alleviating sensitivity to parameters that typically challenge conventional solvers in high-dimensional transient problems. Two benchmark tests are conducted to validate the effectiveness and applicability of the proposed meshless framework for solving 3D nonlinear convection–diffusion–reaction systems.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"172 ","pages":"Article 109722"},"PeriodicalIF":2.8,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144920407","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":"A stochastic column-block gradient descent method for solving nonlinear systems of equations","authors":"Naiyu Jiang,&nbsp;Wendi Bao,&nbsp;Lili Xing,&nbsp;Weiguo Li","doi":"10.1016/j.aml.2025.109735","DOIUrl":"10.1016/j.aml.2025.109735","url":null,"abstract":"<div><div>In this paper, we propose a new stochastic column-block gradient descent method for solving nonlinear systems of equations. It has a descent direction and holds an approximately optimal step size obtained through an optimization problem. We provide a thorough convergence analysis, and derive an upper bound for the convergence rate of the new method. Numerical experiments demonstrate that the proposed method outperforms the existing ones.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"172 ","pages":"Article 109735"},"PeriodicalIF":2.8,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144931722","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}