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The regularity of solution for a generalized Hunter–Saxton type equation 一类广义Hunter-Saxton型方程解的正则性
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-04-06 DOI: 10.1016/j.aml.2025.109561
Hong Cai , Geng Chen , Yannan Shen
{"title":"The regularity of solution for a generalized Hunter–Saxton type equation","authors":"Hong Cai ,&nbsp;Geng Chen ,&nbsp;Yannan Shen","doi":"10.1016/j.aml.2025.109561","DOIUrl":"10.1016/j.aml.2025.109561","url":null,"abstract":"<div><div>The cusp singularity, with only Hölder continuity, is a typical singularity formed in the quasilinear hyperbolic partial differential equations, such as the Hunter–Saxton and Camassa–Holm equations. We establish the global existence of Hölder continuous energy conservative weak solution for a family of Hunter–Saxton type equations, where the regularity of solution varies with respect to a parameter. This result can help us predict regularity of cusp singularity for many other models.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"167 ","pages":"Article 109561"},"PeriodicalIF":2.9,"publicationDate":"2025-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143817234","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}
引用次数: 0
Riemann–Hilbert approach to a new integrable nonlocal fifth-order nonlinear Schrödinger equation with step-like initial data 阶跃初始数据可积非局部五阶非线性Schrödinger方程的Riemann-Hilbert方法
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-04-05 DOI: 10.1016/j.aml.2025.109557
Beibei Hu , Xinru Guan , Ling Zhang
{"title":"Riemann–Hilbert approach to a new integrable nonlocal fifth-order nonlinear Schrödinger equation with step-like initial data","authors":"Beibei Hu ,&nbsp;Xinru Guan ,&nbsp;Ling Zhang","doi":"10.1016/j.aml.2025.109557","DOIUrl":"10.1016/j.aml.2025.109557","url":null,"abstract":"<div><div>In this paper, we investigate the Cauchy problem for a new integrable nonlocal fifth-order nonlinear Schrödinger (FONLS) equation with three free parameters. By solving a 2 × 2 matrix Riemann–Hilbert problem in the complex <span><math><mi>k</mi></math></span>-plane, we obtain the limit form solutions of the nonlocal FONLS equation. As an example, we provide an exact expression of the one-soliton solution for the nonlocal FONLS equation by the Riemann–Hilbert problem in special cases.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"167 ","pages":"Article 109557"},"PeriodicalIF":2.9,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143785930","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}
引用次数: 0
The first eigenvalue of polyharmonic operators and its applications 多谐算子的第一特征值及其应用
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-04-01 DOI: 10.1016/j.aml.2025.109559
Meiqiang Feng, Yichen Lu
{"title":"The first eigenvalue of polyharmonic operators and its applications","authors":"Meiqiang Feng,&nbsp;Yichen Lu","doi":"10.1016/j.aml.2025.109559","DOIUrl":"10.1016/j.aml.2025.109559","url":null,"abstract":"<div><div>In this paper, our main purpose is to prove the existence of the first eigenvalue for the polyharmonic operator with Navier boundary conditions. In addition, the corresponding eigenfunction is demonstrated to be positive. As an application, we will discuss a necessary condition for the existence of positive solutions to some polyharmonic problems on the first eigenvalue.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"167 ","pages":"Article 109559"},"PeriodicalIF":2.9,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761338","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}
引用次数: 0
Asymptotic profile of steady states for a partially degenerate Aedes aegypti population model 部分退化埃及伊蚊种群模型稳态的渐近分布
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-03-30 DOI: 10.1016/j.aml.2025.109554
Jie Xing, Hua Nie
{"title":"Asymptotic profile of steady states for a partially degenerate Aedes aegypti population model","authors":"Jie Xing,&nbsp;Hua Nie","doi":"10.1016/j.aml.2025.109554","DOIUrl":"10.1016/j.aml.2025.109554","url":null,"abstract":"<div><div>This paper explores the asymptotic profile of steady states in a partially degenerate Aedes aegypti population model within advective environments. By reducing the model to a scalar equation, we establish the existence and uniqueness of positive steady-state solutions using the method of upper and lower solutions. We analyze the interaction between diffusion and advection, focusing on their effects on the species’ spatial distribution. Specifically, we examine how variations in diffusion and advection rates impact the asymptotic profiles. Our results show that high advection rates and low diffusion rates lead to species concentration downstream. These findings provide important insights into Aedes aegypti population dynamics in bounded domains, highlighting the critical roles of advection and diffusion in shaping spatial patterns of the species.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"167 ","pages":"Article 109554"},"PeriodicalIF":2.9,"publicationDate":"2025-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761328","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}
引用次数: 0
Conservative Crank–Nicolson-type and compact finite difference schemes for modeling the Schrödinger equation with point nonlinearity 具有点非线性的Schrödinger方程的保守crank - nicolson型和紧致有限差分格式
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-03-28 DOI: 10.1016/j.aml.2025.109553
Yong Wu , Fenghua Tong , Xuanxuan Zhou , Yongyong Cai
{"title":"Conservative Crank–Nicolson-type and compact finite difference schemes for modeling the Schrödinger equation with point nonlinearity","authors":"Yong Wu ,&nbsp;Fenghua Tong ,&nbsp;Xuanxuan Zhou ,&nbsp;Yongyong Cai","doi":"10.1016/j.aml.2025.109553","DOIUrl":"10.1016/j.aml.2025.109553","url":null,"abstract":"<div><div>In this paper, we propose conservative Crank–Nicolson-type and compact finite difference schemes for the nonlinear Schrödinger equation with point nonlinearity. To construct these schemes, we first transform the point nonlinearity into an interface condition, then decompose the computational domain along the interface into two subregions with a jump condition. Different discretization approximations of the jump condition lead to different numerical schemes. For the Crank–Nicolson finite difference scheme, we prove its unconditional mass conservation and energy conservation. Some numerical examples are also presented to illustrate the accuracy and efficiency of our proposed schemes.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"167 ","pages":"Article 109553"},"PeriodicalIF":2.9,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761329","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}
引用次数: 0
A preconditioning technique of Gauss–Legendre quadrature for the logarithm of symmetric positive definite matrices 对称正定矩阵对数的高斯-勒让德正交预处理技术
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-03-25 DOI: 10.1016/j.aml.2025.109552
Fuminori Tatsuoka, Tomohiro Sogabe, Tomoya Kemmochi, Shao-Liang Zhang
{"title":"A preconditioning technique of Gauss–Legendre quadrature for the logarithm of symmetric positive definite matrices","authors":"Fuminori Tatsuoka,&nbsp;Tomohiro Sogabe,&nbsp;Tomoya Kemmochi,&nbsp;Shao-Liang Zhang","doi":"10.1016/j.aml.2025.109552","DOIUrl":"10.1016/j.aml.2025.109552","url":null,"abstract":"<div><div>This note considers the computation of the logarithm of symmetric positive definite matrices using the Gauss–Legendre (GL) quadrature. The GL quadrature becomes slow when the condition number of the given matrix is large. In this note, we propose a technique dividing the matrix logarithm into two matrix logarithms, where the condition numbers of the divided logarithm arguments are smaller than that of the original matrix. Although the matrix logarithm needs to be computed twice, each computation can be performed more efficiently, and it potentially reduces the overall computational cost. It is shown that the proposed technique is effective when the condition number of the given matrix is approximately between 130 and <span><math><mrow><mn>3</mn><mo>.</mo><mn>0</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>5</mn></mrow></msup></mrow></math></span>.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"167 ","pages":"Article 109552"},"PeriodicalIF":2.9,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143714660","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}
引用次数: 0
On absolute value equations associated with M-matrices and H-matrices 关于与[公式省略]-矩阵和[公式省略]-矩阵相关的绝对值方程
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-03-19 DOI: 10.1016/j.aml.2025.109550
Chun-Hua Guo
{"title":"On absolute value equations associated with M-matrices and H-matrices","authors":"Chun-Hua Guo","doi":"10.1016/j.aml.2025.109550","DOIUrl":"10.1016/j.aml.2025.109550","url":null,"abstract":"<div><div>We consider the absolute value equation (AVE) <span><math><mrow><mi>A</mi><mi>x</mi><mo>−</mo><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow><mo>=</mo><mi>b</mi></mrow></math></span>, where the diagonal entries of <span><math><mrow><mi>A</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow></msup></mrow></math></span> are all greater than 1 and <span><math><mrow><mrow><mo>〈</mo><mi>A</mi><mo>〉</mo></mrow><mo>−</mo><mi>I</mi></mrow></math></span> is an irreducible singular <span><math><mi>M</mi></math></span>-matrix (<span><math><mrow><mo>〈</mo><mi>A</mi><mo>〉</mo></mrow></math></span> is the comparison matrix of <span><math><mi>A</mi></math></span>). We investigate the existence and uniqueness of solutions for the AVE. The AVE does not necessarily have a unique solution for every <span><math><mrow><mi>b</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></math></span>, so most of the existing convergence results for various iterative methods are not generally applicable. Moreover, the generalized Newton method may break down. We show that if the AVE has a solution <span><math><msup><mrow><mi>x</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span> with at least one negative component, then the sequence generated by the generalized Gauss–Seidel iteration converges to <span><math><msup><mrow><mi>x</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span> linearly for any initial vector.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109550"},"PeriodicalIF":2.9,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143675633","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}
引用次数: 0
On the linear independence condition for the Bobkov-Tanaka first eigenvalue of the double-phase operator 双相算子Bobkov-Tanaka第一特征值的线性无关条件
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-03-19 DOI: 10.1016/j.aml.2025.109549
Nirjan Biswas , Laura Gambera , Umberto Guarnotta
{"title":"On the linear independence condition for the Bobkov-Tanaka first eigenvalue of the double-phase operator","authors":"Nirjan Biswas ,&nbsp;Laura Gambera ,&nbsp;Umberto Guarnotta","doi":"10.1016/j.aml.2025.109549","DOIUrl":"10.1016/j.aml.2025.109549","url":null,"abstract":"<div><div>The paper investigates a pivotal condition for the Bobkov-Tanaka type spectrum for double-phase operators. This condition is satisfied if either the weight <span><math><mi>w</mi></math></span> driving the double-phase operator is strictly positive in the whole domain or the domain is convex and fulfils a suitable symmetry condition.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109549"},"PeriodicalIF":2.9,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143675634","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}
引用次数: 0
Asymptotical stability of a stochastic SIQRS epidemic model with log-normal Ornstein–Uhlenbeck process 具有对数正态Ornstein-Uhlenbeck过程的SIQRS流行病随机模型的渐近稳定性
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-03-19 DOI: 10.1016/j.aml.2025.109551
Xiao Li, Qun Liu
{"title":"Asymptotical stability of a stochastic SIQRS epidemic model with log-normal Ornstein–Uhlenbeck process","authors":"Xiao Li,&nbsp;Qun Liu","doi":"10.1016/j.aml.2025.109551","DOIUrl":"10.1016/j.aml.2025.109551","url":null,"abstract":"<div><div>In this work, we propose and analyze a stochastic SIQRS epidemic model with the disease transmission rate driven by a log-normal Ornstein–Uhlenbeck process. By establishing a series of Lyapunov functions, we derive sufficient criteria for the asymptotical stability of the positive equilibrium of the system which suggests the prevalence of the disease in the long term. This work provides a basis for taking measures to control the disease dynamics.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109551"},"PeriodicalIF":2.9,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143675608","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}
引用次数: 0
Global dynamics of a two-stage social insect model incorporating nonlinear egg cannibalism 包含非线性虫卵同类相食的两阶段社会昆虫模型的全局动力学
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-03-19 DOI: 10.1016/j.aml.2025.109533
Tao Feng, Xinyu Wu
{"title":"Global dynamics of a two-stage social insect model incorporating nonlinear egg cannibalism","authors":"Tao Feng,&nbsp;Xinyu Wu","doi":"10.1016/j.aml.2025.109533","DOIUrl":"10.1016/j.aml.2025.109533","url":null,"abstract":"<div><div>This study refines the two-stage social insect model of Kang et al. (2015) by incorporating a nonlinear egg cannibalism rate. The introduction of nonlinearity presents analytical challenges, addressed through the application of the compound matrix method to rigorously establish global stability. The analysis reveals complex dynamical behaviors, including two distinct types of bistability: one between extinction and coexistence equilibria, and another between low-density and high-density coexistence equilibria. These findings underscore the ecological importance of nonlinear egg cannibalism in shaping population dynamics and enhancing species persistence under resource-limited conditions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109533"},"PeriodicalIF":2.9,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143675635","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}
引用次数: 0
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