Applied Mathematics Letters最新文献

{"title":"Improvement of conditions for global solvability in a chemotaxis system with signal-dependent motility and generalized logistic source","authors":"Changfeng Liu , Jianping Gao","doi":"10.1016/j.aml.2025.109470","DOIUrl":"10.1016/j.aml.2025.109470","url":null,"abstract":"<div><div>This paper deals with a chemotaxis system with signal-dependent motility <span><math><mfenced><mrow><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mo>∇</mo><mi>⋅</mi><mrow><mo>(</mo><mi>γ</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>∇</mo><mi>u</mi><mo>)</mo></mrow><mo>−</mo><mo>∇</mo><mi>⋅</mi><mrow><mo>(</mo><mi>χ</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mi>u</mi><mo>∇</mo><mi>v</mi><mo>)</mo></mrow><mo>+</mo><mi>λ</mi><mi>u</mi><mo>−</mo><mi>μ</mi><msup><mrow><mi>u</mi></mrow><mrow><mi>l</mi></mrow></msup><mspace></mspace></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><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><mi>u</mi><mspace></mspace></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>∂</mi></mrow><mrow><mi>ν</mi></mrow></msub><mi>u</mi><mo>=</mo><msub><mrow><mi>∂</mi></mrow><mrow><mi>ν</mi></mrow></msub><mi>v</mi><mo>=</mo><mn>0</mn><mspace></mspace></mtd><mtd><mi>x</mi><mo>∈</mo><mi>∂</mi><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><mi>u</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mn>0</mn><mo>)</mo></mrow><mo>=</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>≥</mo><mn>0</mn><mo>,</mo><mspace></mspace><mspace></mspace><mspace></mspace><mi>v</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mn>0</mn><mo>)</mo></mrow><mo>=</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>≥</mo><mn>0</mn><mspace></mspace></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span> under homogeneous Neumann boundary conditions in a bounded domain <span><math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></math></span> <span><math><mrow><mo>(</mo><mi>n</mi><mo>></mo><mn>2</mn><mo>)</mo></mrow></math></span>. If <span><math><mrow><mi>λ</mi><mo>∈</mo><mi>R</mi></mrow></math></span> and <span><math><mrow><mi>μ</mi><mo>></mo><mn>0</mn></mrow></math></span> are constants, we prove that this problem possesses a global classical solution that is uniformly bounded under the conditions that <span><math><mrow><mi>l</mi><mo>></mo><mo>min</mo><mfenced><mrow><mn>3</mn><mo>,</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></mfenced><mo>.</mo></mrow></math></span> This result partially improved the work of Lv and Wang (Proc Roy Soc Edinburgh Sect A. 2021, 151 (2): 821-841), in which, the global boundedness of solution is established for <span><math><mrow><mi>l</mi><mo>></mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mf","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109470"},"PeriodicalIF":2.9,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143077704","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":"Dispersive shock waves in the fifth-order modified KdV equation","authors":"Dong-Rao Jing,&nbsp;Hai-Qiang Zhang,&nbsp;Nan-Nan Wei","doi":"10.1016/j.aml.2025.109468","DOIUrl":"10.1016/j.aml.2025.109468","url":null,"abstract":"<div><div>This study focuses on the Whitham modulation theory of the fifth-order modified KdV equation (5mKdV), successfully deriving the solutions for modulated periodic waves and establishing corresponding Whitham equations. Through the detailed analysis of the initial step solution, the rarefaction waves and two types of dispersive shock wave structures are revealed. Our results not only enrich the theoretical system of the 5mKdV equation but also provide valuable theoretical support for the analysis and control of wave phenomena.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109468"},"PeriodicalIF":2.9,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143035230","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 Hermite method of approximate particular solutions for solving the Poisson equation","authors":"Kwesi Acheampong,&nbsp;Huiqing Zhu","doi":"10.1016/j.aml.2025.109471","DOIUrl":"10.1016/j.aml.2025.109471","url":null,"abstract":"<div><div>In this paper, we propose a localized Hermite method of approximate particular solutions (LHMAPS) for solving the Poisson equation. Unlike the localized method of approximate particular solutions (LMAPS) that approximates only function values of the solution in different local neighborhoods of collocation nodes by using particular solutions of radial basis functions, the proposed method employs mixed basis functions, combining radial basis functions and their particular solutions for the Laplace operator within local stencils to simultaneously approximate both the solution and its Laplacian. Numerical experiments show that significantly improves the accuracy of LMAPS.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109471"},"PeriodicalIF":2.9,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143077671","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 class of higher-order time-splitting Monte Carlo method for fractional Allen–Cahn equation","authors":"Huifang Yuan ,&nbsp;Zhiyuan Hui","doi":"10.1016/j.aml.2025.109467","DOIUrl":"10.1016/j.aml.2025.109467","url":null,"abstract":"<div><div>In this paper, we introduce a novel class of higher-order time-splitting Monte Carlo method tailored for both fractional and classical Allen–Cahn equations. The proposed method integrates the spectral Monte Carlo method (SMC) with a time-splitting scheme, alternating between efficiently computing the linear propagator via the spectral Monte Carlo method and explicitly evaluating the nonlinear propagator. Numerical results for various <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>]</mo></mrow></mrow></math></span> demonstrate the method’s ability to achieve first-, second-, and fourth-order convergence rates, thereby confirming its effectiveness and accuracy.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109467"},"PeriodicalIF":2.9,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143035329","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 oscillation of second-order functional differential equations with a delayed damping term","authors":"Osama Moaaz ,&nbsp;Higinio Ramos","doi":"10.1016/j.aml.2025.109464","DOIUrl":"10.1016/j.aml.2025.109464","url":null,"abstract":"<div><div>In this work, we derive some criteria for studying the asymptotic and oscillatory behavior of solutions of functional differential equations with a delayed damping term. Our results extend and improve upon the limited prior research on this type of equations. The primary goal is to derive criteria applicable to both ordinary and non-damped cases, while accounting for the effects of delay functions. Additionally, unlike previous studies, we provide criteria that ensure the oscillation of all solutions. The significance of these results is illustrated through remarks and examples.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109464"},"PeriodicalIF":2.9,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143035202","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":"Leighton–Wintner-type oscillation theorem for the discrete p(k)-Laplacian","authors":"Kōdai Fujimoto ,&nbsp;Kazuki Ishibashi ,&nbsp;Masakazu Onitsuka","doi":"10.1016/j.aml.2025.109465","DOIUrl":"10.1016/j.aml.2025.109465","url":null,"abstract":"<div><div>This paper addresses oscillation problems for difference equations with a discrete <span><math><mrow><mi>p</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></math></span>-Laplacian. In general, applying the Riccati technique to discrete oscillations is difficult. However, this study established a Leighton–Wintner-type oscillation theorem using the Riccati technique. Three examples are provided to illustrate the results. In particular, we examined the oscillatory problem for a certain nonlinear difference equation, including the Harper model, and demonstrated that the solutions are oscillatory even when <span><math><mrow><mi>p</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></math></span> diverges to infinity.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109465"},"PeriodicalIF":2.9,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990380","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 relation between the exponential of real matrices and that of dual matrices","authors":"Chengdong Liu ,&nbsp;Yimin Wei ,&nbsp;Pengpeng Xie","doi":"10.1016/j.aml.2025.109466","DOIUrl":"10.1016/j.aml.2025.109466","url":null,"abstract":"<div><div>Dual number matrices play a significant role in engineering applications such as kinematics and dynamics. The matrix exponential is ubiquitous in screw-based kinematics. In this paper, we develop an explicit formula for the dual matrix exponential. The result is closely related to the Fréchet derivative, which can be formed by the standard part and dual part of the original matrix. We only need to compute the exponential of a real matrix. Then, we give a formula of computing the dual quaternion matrix exponential. Our results are illustrated through a practical example from robotic kinematics.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109466"},"PeriodicalIF":2.9,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990379","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":"Geometric programming for multilinear systems with nonsingular M-tensors","authors":"Haibin Chen ,&nbsp;Guanglu Zhou ,&nbsp;Hong Yan","doi":"10.1016/j.aml.2025.109462","DOIUrl":"10.1016/j.aml.2025.109462","url":null,"abstract":"<div><div>We consider multilinear systems which arise in various applications, such as data mining and numerical differential equations. In this paper, we show that the multilinear system with a nonsingular <span><math><mi>M</mi></math></span>-tensor can be formulated equivalently into a geometric programming (GP) problem which can be solved by the barrier-based interior point method with a worst-case polynomial-time complexity. To the best of our knowledge, there is not a complexity analysis for the existing algorithms of the multilinear systems. Numerical results are reported to show the efficiency of the proposed GP method.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109462"},"PeriodicalIF":2.9,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990387","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 decay rate to the contact discontinuity for Navier–Stokes equations under generic perturbations","authors":"Lingjun Liu ,&nbsp;Guiqin Qiu ,&nbsp;Shu Wang ,&nbsp;Lingda Xu","doi":"10.1016/j.aml.2025.109461","DOIUrl":"10.1016/j.aml.2025.109461","url":null,"abstract":"<div><div>This paper investigates the large-time asymptotic behavior of contact waves in 1-D compressible Navier–Stokes equations. We derive the optimal decay rate for generic initial perturbations, meaning the perturbation’s integral does not need to be zero. It is well-known that generic perturbations in Navier–Stokes equations generate diffusion waves, implying that the optimal decay rate for contact waves in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span>-norm is <span><math><msup><mrow><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></math></span>. However, the presence of diffusion waves introduces error terms, leading to energy growth in the anti-derivatives of the perturbations. Furthermore, studying contact waves depends on certain structural conditions, which hold for the original system but not for its derivative systems. This makes it challenging to obtain accurate estimates for the energy of the derivatives.</div><div>In this paper, we refine the estimates for both anti-derivatives and the original perturbations. We then introduce an innovative transformation to ensure that the structural conditions continue to hold for the system of derivatives. With this approach, we achieve better estimates for the derivatives, leading to the optimal decay rates. This result improves upon the well-known findings of Huang et al. (2008), and the method has the potential for application in more general systems.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109461"},"PeriodicalIF":2.9,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990414","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":"Stability analysis of a conservative reaction–diffusion system with rate controls","authors":"Jie Ding ,&nbsp;Fei Xu ,&nbsp;Zhi Ling","doi":"10.1016/j.aml.2025.109457","DOIUrl":"10.1016/j.aml.2025.109457","url":null,"abstract":"<div><div>This paper demonstrates the fundamental properties of a conservative reaction–diffusion system. The solution of the system exists globally and is unique, as well as uniformly converges to its constant equilibrium as time tends to infinity. In addition, the steady-state system only has a constant solution under a mass conservation condition.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109457"},"PeriodicalIF":2.9,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990279","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}