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Local-in-space blow-up of a weakly dissipative generalized Dullin–Gottwald–Holm equation 一类弱耗散广义Dullin-Gottwald-Holm方程的空间局部爆破
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-12-26 DOI: 10.1016/j.aml.2024.109445
Wenguang Cheng, Bingqi Li
{"title":"Local-in-space blow-up of a weakly dissipative generalized Dullin–Gottwald–Holm equation","authors":"Wenguang Cheng,&nbsp;Bingqi Li","doi":"10.1016/j.aml.2024.109445","DOIUrl":"10.1016/j.aml.2024.109445","url":null,"abstract":"<div><div>This paper addresses the problems of blow-up for a weakly dissipative generalized Dullin–Gottwald–Holm equation. A new sufficient condition on the initial data is provided to ensure the finite time local-in-space blow-up of strong solutions, which improves the local-in-space blow-up result of Novruzov and Yazar <span><span>[1]</span></span>.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109445"},"PeriodicalIF":2.9,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889271","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
Constructing solutions of the ‘bad’ Jaulent–Miodek equation based on a relationship with the Burgers equation 基于与Burgers方程的关系，构造bad Jaulent-Miodek方程的解
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-12-26 DOI: 10.1016/j.aml.2024.109440
Jing-Jing Su, Yu-Long He, Bo Ruan
{"title":"Constructing solutions of the ‘bad’ Jaulent–Miodek equation based on a relationship with the Burgers equation","authors":"Jing-Jing Su,&nbsp;Yu-Long He,&nbsp;Bo Ruan","doi":"10.1016/j.aml.2024.109440","DOIUrl":"10.1016/j.aml.2024.109440","url":null,"abstract":"<div><div>The ‘bad’ Jaulent–Miodek (JM) equation describes the wave evolution of inviscid shallow water over a flat bottom in the presence of shear, which is ill-posed and unstable so that its general initial problem on the zero plane is difficult to solve through traditional mesh-based numerical methods. In this paper, using the Darboux transformation, we find a relation between the ‘bad’ JM equation and the well-known Burgers equation. Based on the Burgers equation, we construct the analytical and numerical solutions of the ‘bad’ JM equation via the Hirota bilinear method and the time-splitting Fourier spectral method. Specifically, we numerically present the interaction between two Gaussian packets of the ‘bad’ JM equation. This approach extends the applicability of traditional numerical methods for solving general initial problems of the ‘bad’ JM equation.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109440"},"PeriodicalIF":2.9,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889360","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 second-order accurate numerical method with unconditional energy stability for the Lifshitz–Petrich equation on curved surfaces 曲面上Lifshitz-Petrich方程的一种具有无条件能量稳定的二阶精确数值方法
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-12-24 DOI: 10.1016/j.aml.2024.109439
Xiaochuan Hu , Qing Xia , Binhu Xia , Yibao Li
{"title":"A second-order accurate numerical method with unconditional energy stability for the Lifshitz–Petrich equation on curved surfaces","authors":"Xiaochuan Hu ,&nbsp;Qing Xia ,&nbsp;Binhu Xia ,&nbsp;Yibao Li","doi":"10.1016/j.aml.2024.109439","DOIUrl":"10.1016/j.aml.2024.109439","url":null,"abstract":"<div><div>In this paper, we introduce an efficient numerical algorithm for solving the Lifshitz–Petrich equation on closed surfaces. The algorithm involves discretizing the surface with a triangular mesh, allowing for an explicit definition of the Laplace–Beltrami operator based on the neighborhood information of the mesh elements. To achieve second-order temporal accuracy, the backward differentiation formula scheme and the scalar auxiliary variable method are employed for Lifshitz–Petrich equation. The discrete system is subsequently solved using the biconjugate gradient stabilized method, with incomplete LU decomposition of the coefficient matrix serving as a preprocessor. The proposed algorithm is characterized by its simplicity in implementation and second-order precision in both spatial and temporal domains. Numerical experiments are conducted to validate the unconditional energy stability and efficacy of the algorithm.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109439"},"PeriodicalIF":2.9,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889361","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
An unstructured algorithm for the singular value decomposition of biquaternion matrices 双四元数矩阵奇异值分解的非结构化算法
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-12-21 DOI: 10.1016/j.aml.2024.109436
Gang Wang
{"title":"An unstructured algorithm for the singular value decomposition of biquaternion matrices","authors":"Gang Wang","doi":"10.1016/j.aml.2024.109436","DOIUrl":"10.1016/j.aml.2024.109436","url":null,"abstract":"<div><div>With the modeling of the biquaternion algebra in multidimensional signal processing, it has become possible to address issues such as data separation, denoising, and anomaly detection. This paper investigates the singular value decomposition of biquaternion matrices (SVDBQ), establishing an SVDBQ theorem that ensures unitary matrices formed by the left and right singular vectors, while also introducing a new form for singular values. Additionally, the non-uniqueness of SVDBQ is proven, expanding the theoretical framework of the biquaternion algebra. Building on this foundation, the paper presents a novel, fast, unstructured algorithm based on the isomorphic representation matrices of biquaternion matrices. Unlike existing methods, which are often complex and computationally expensive, the proposed algorithm is structurally simple and significantly faster, making it ideal for real-time signal processing. Numerical experiments validate the efficiency and effectiveness of this new algorithm, demonstrating its potential to advance both research and practical applications in signal processing.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109436"},"PeriodicalIF":2.9,"publicationDate":"2024-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889256","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
Uniqueness of identifying multiple parameters in a time-fractional Cattaneo equation 时间分数型Cattaneo方程中辨识多参数的唯一性
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-12-21 DOI: 10.1016/j.aml.2024.109438
Yun Zhang, Xiaoli Feng
{"title":"Uniqueness of identifying multiple parameters in a time-fractional Cattaneo equation","authors":"Yun Zhang,&nbsp;Xiaoli Feng","doi":"10.1016/j.aml.2024.109438","DOIUrl":"10.1016/j.aml.2024.109438","url":null,"abstract":"<div><div>This paper addresses an inverse problem involving the simultaneous identification of the fractional order, potential coefficient, initial value and source term in a time-fractional Cattaneo equation. Utilizing the method of Laplace transformation, we demonstrate that the multiple unknowns can be uniquely determined from observational data collected at two boundary points.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109438"},"PeriodicalIF":2.9,"publicationDate":"2024-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889362","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 trapped lee waves with centripetal forces 利用向心力研究被困背风波
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-12-20 DOI: 10.1016/j.aml.2024.109435
Tao Li, JinRong Wang
{"title":"On trapped lee waves with centripetal forces","authors":"Tao Li,&nbsp;JinRong Wang","doi":"10.1016/j.aml.2024.109435","DOIUrl":"10.1016/j.aml.2024.109435","url":null,"abstract":"<div><div>This paper firstly studies exact solutions to the atmospheric equations of motion in the <span><math><mi>f</mi></math></span>-plane and <span><math><mi>β</mi></math></span>-plane approximations while considering centripetal forces. The obtained solutions are shown in Lagrangian coordinates. Additionally, we derive the dispersion relations and perform a qualitative analysis of density, pressure, and vorticity.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109435"},"PeriodicalIF":2.9,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889363","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
Lyapunov functions for some epidemic model with high risk and vaccinated class 一类具有高风险和接种类的传染病模型的Lyapunov函数
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-12-19 DOI: 10.1016/j.aml.2024.109437
Ran Zhang, Xue Ren
{"title":"Lyapunov functions for some epidemic model with high risk and vaccinated class","authors":"Ran Zhang,&nbsp;Xue Ren","doi":"10.1016/j.aml.2024.109437","DOIUrl":"10.1016/j.aml.2024.109437","url":null,"abstract":"<div><div>This paper considers the global asymptotic stability of a model with epidemic model with high risk and vaccinated class, and extends the related methods to two case of reaction–diffusion equations. The results presented here generalize those from Movahedi (2024).</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109437"},"PeriodicalIF":2.9,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889364","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
Stability and Turing bifurcation in a non-local reaction–diffusion equation with a top-hat kernel 一类具有顶帽核的非局部反应扩散方程的稳定性和图灵分岔
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-12-19 DOI: 10.1016/j.aml.2024.109433
Ying Li, Yongli Song
{"title":"Stability and Turing bifurcation in a non-local reaction–diffusion equation with a top-hat kernel","authors":"Ying Li,&nbsp;Yongli Song","doi":"10.1016/j.aml.2024.109433","DOIUrl":"10.1016/j.aml.2024.109433","url":null,"abstract":"<div><div>In the non-local reaction–diffusion equation, the form of the kernel function has an important effect on the dynamics of the equation. In this paper, we study the spatiotemporal dynamics of a class of non-local reaction–diffusion equation where the non-locality is described by the top-hat function with the perceptual radius. The perceptual radius establishes a bridge between the local equation and global equation. It has been shown that the perceptual radius can destabilize the constant steady state via Turing bifurcation and the critical bifurcation value is theoretically determined.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109433"},"PeriodicalIF":2.9,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889365","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
Lattice Boltzmann method for surface quasi-geostrophic equations with fractional Laplacian 带分数阶拉普拉斯的曲面拟地转方程的点阵Boltzmann方法
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-12-19 DOI: 10.1016/j.aml.2024.109434
Haoyuan Gong , Tongtong Zhou , Baochang Shi , Rui Du
{"title":"Lattice Boltzmann method for surface quasi-geostrophic equations with fractional Laplacian","authors":"Haoyuan Gong ,&nbsp;Tongtong Zhou ,&nbsp;Baochang Shi ,&nbsp;Rui Du","doi":"10.1016/j.aml.2024.109434","DOIUrl":"10.1016/j.aml.2024.109434","url":null,"abstract":"<div><div>The surface quasi-geostrophic equations with fractional Laplacian are important in the field of oceanic and atmospheric dynamics. In this paper, a new lattice Boltzmann model is proposed to solve the equations. We first obtain an approximation of the governing equation based on the Fourier transform and Gaussian quadrature formula. An LBGK model with a suitable equilibrium distribution function is then developed for the problem. Through Chapman–Enskog expansion, the approximated macroscopic equations can be recovered from the lattice Boltzmann model. Numerical simulations are carried out to verify the numerical accuracy and efficiency.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109434"},"PeriodicalIF":2.9,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142929323","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 attractor for an age-structured HIV model with nonlinear incidence rate 具有非线性发病率的年龄结构HIV模型的全局吸引子
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-12-18 DOI: 10.1016/j.aml.2024.109428
Ru Meng , Tingting Zheng , Yantao Luo , Zhidong Teng
{"title":"Global attractor for an age-structured HIV model with nonlinear incidence rate","authors":"Ru Meng ,&nbsp;Tingting Zheng ,&nbsp;Yantao Luo ,&nbsp;Zhidong Teng","doi":"10.1016/j.aml.2024.109428","DOIUrl":"10.1016/j.aml.2024.109428","url":null,"abstract":"<div><div>Using the method of characteristics and defining one auxiliary function, we prove the existence of global attractor for a general age-structured HIV model, which can be used to solve the uniformly persistence problem in the Kumar and Abbas (2022).</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109428"},"PeriodicalIF":2.9,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874398","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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