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Oscillation criteria for the second-order neutral advanced dynamic equations on time scales
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-03-10 DOI: 10.1016/j.aml.2025.109543
Ying Sui
{"title":"Oscillation criteria for the second-order neutral advanced dynamic equations on time scales","authors":"Ying Sui","doi":"10.1016/j.aml.2025.109543","DOIUrl":"10.1016/j.aml.2025.109543","url":null,"abstract":"<div><div>In this paper, we consider the oscillation of second-order neutral advanced dynamic equations on time scales of the form <span><math><mrow><msup><mrow><mrow><mo>(</mo><mi>r</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><msup><mrow><mrow><mo>(</mo><msup><mrow><mi>z</mi></mrow><mrow><mi>Δ</mi></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow><mrow><mi>α</mi></mrow></msup><mo>)</mo></mrow></mrow><mrow><mi>Δ</mi></mrow></msup><mo>+</mo><mi>q</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>f</mi><mrow><mo>(</mo><mi>y</mi><mrow><mo>(</mo><mi>m</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>)</mo></mrow><mo>=</mo><mn>0</mn><mo>,</mo></mrow></math></span> where <span><math><mrow><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mi>y</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>+</mo><mi>p</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>y</mi><mrow><mo>(</mo><mi>τ</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>m</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>≥</mo><mi>t</mi></mrow></math></span>. We consider two cases of <span><math><mrow><mi>τ</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>≥</mo><mi>t</mi></mrow></math></span> and <span><math><mrow><mi>τ</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>≤</mo><mi>t</mi></mrow></math></span>, respectively. Some new oscillatory results are based on the new comparison theorems that enable us to reduce problem of the oscillation of the second-order equations to the oscillation of the first-order equations.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109543"},"PeriodicalIF":2.9,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143601641","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 super-localized finite element method for inhomogeneous fourth-order singular perturbation problem
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-03-10 DOI: 10.1016/j.aml.2025.109534
Bin Dai, Chen-Song Zhang
{"title":"A super-localized finite element method for inhomogeneous fourth-order singular perturbation problem","authors":"Bin Dai,&nbsp;Chen-Song Zhang","doi":"10.1016/j.aml.2025.109534","DOIUrl":"10.1016/j.aml.2025.109534","url":null,"abstract":"<div><div>This paper presents a multi-scale method for inhomogeneous fourth-order singular perturbation problems. This method guarantees a uniform high-order convergence rate, regardless of the presence of multi-scale coefficients or boundary layer effects. The numerical experiments in two and three dimensions confirm the theory.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109534"},"PeriodicalIF":2.9,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143628821","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 fast wavelet collocation method with compression techniques for Steklov eigenvalue problems of Helmholtz equations
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-03-10 DOI: 10.1016/j.aml.2025.109532
Guangqing Long , Huanfeng Yang , Li-Bin Liu
{"title":"A fast wavelet collocation method with compression techniques for Steklov eigenvalue problems of Helmholtz equations","authors":"Guangqing Long ,&nbsp;Huanfeng Yang ,&nbsp;Li-Bin Liu","doi":"10.1016/j.aml.2025.109532","DOIUrl":"10.1016/j.aml.2025.109532","url":null,"abstract":"<div><div>A fast wavelet collocation method with compression techniques is proposed for solving the Steklov eigenvalue problem. Based on the potential theory, the Steklov eigenvalue problem is reformulated as a boundary integral equation with logarithmic singularity. By using the compression technique, the wavelet coefficient matrix is truncated into sparse. This technique leads to the algorithm faster. We show that the proposed method requires only linear computational complexity and has the optimal convergence order for the approximate eigenvalues and eigenfunctions. The numerical examples are provided and analyzed.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109532"},"PeriodicalIF":2.9,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143610323","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
Computational analysis of a normalized time-fractional Fisher equation
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-03-08 DOI: 10.1016/j.aml.2025.109542
Soobin Kwak , Yunjae Nam , Seungyoon Kang , Junseok Kim
{"title":"Computational analysis of a normalized time-fractional Fisher equation","authors":"Soobin Kwak ,&nbsp;Yunjae Nam ,&nbsp;Seungyoon Kang ,&nbsp;Junseok Kim","doi":"10.1016/j.aml.2025.109542","DOIUrl":"10.1016/j.aml.2025.109542","url":null,"abstract":"<div><div>This study presents a normalized time-fractional Fisher equation to resolve scaling inconsistencies associated with conventional time-fractional derivatives. A finite difference scheme is applied to numerically solve the equation. Computational experiments are conducted to investigate the impact of the fractional order on the system’s dynamics. The numerical results demonstrate the influence of memory effects on the solution’s evolution and highlight the advantages of the proposed normalization approach for fractional-order models.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109542"},"PeriodicalIF":2.9,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143592333","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
Analytical 3D fundamental solutions for dynamic saturated poroelasticity
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-03-06 DOI: 10.1016/j.aml.2025.109547
Tao Deng, Xinhui Chen, Wenjun Luo, Xing Wei
{"title":"Analytical 3D fundamental solutions for dynamic saturated poroelasticity","authors":"Tao Deng,&nbsp;Xinhui Chen,&nbsp;Wenjun Luo,&nbsp;Xing Wei","doi":"10.1016/j.aml.2025.109547","DOIUrl":"10.1016/j.aml.2025.109547","url":null,"abstract":"<div><div>The fundamental solution is a particular solution of the inhomogeneous equation with Dirac delta function as the right hand side term. It holds significant importance in both applied and theoretical mathematics and physics. This study focuses on deriving 3D fundamental solutions in the frequency domain for wave propagation in a fluid-saturated porous medium in the context of Biot's theory. The approach begins with the Helmholtz decomposition, which decomposes the variables into three scalar potentials. These potentials are then decoupled and determined via matrix eigenvalue analysis. Based on the derived potentials, the fundamental solutions for displacements and pressure are derived. Finally, the applicability of the fundamental solutions is verified via 3D cases through the method of fundamental solutions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109547"},"PeriodicalIF":2.9,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143592332","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
Analytical solution to the elastic wave scattering problem caused by a circular inclusion in two dimensional layered inhomogeneous piezoelectric media
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-03-05 DOI: 10.1016/j.aml.2025.109546
Enxiang Qu , Hui Qi , Jing Guo
{"title":"Analytical solution to the elastic wave scattering problem caused by a circular inclusion in two dimensional layered inhomogeneous piezoelectric media","authors":"Enxiang Qu ,&nbsp;Hui Qi ,&nbsp;Jing Guo","doi":"10.1016/j.aml.2025.109546","DOIUrl":"10.1016/j.aml.2025.109546","url":null,"abstract":"<div><div>The method of complex variable functions is integrated to investigate the steady state problem wherein SH guided waves impinge upon two dimensional layered inhomogeneous piezoelectric media with a circular inclusion, and the corresponding analytical expressions are derived. Specifically, the guided wave expansion technique is employed to formulate the incident wave field of planar SH guided waves. By coupling with the multiple mirror method, the scattering wave field that complies with the requirements of two infinitely long straight boundaries is ascertained. It should be emphasized that these layered straight boundaries must fulfill the stress free and electrically insulating conditions. Subsequently, based on the boundary conditions of stress free, displacement continuity, potential and normal electric displacement continuity that a circular inclusion need to satisfy, infinite linear algebraic equations are further established. Finally, the mathematical analytical expressions for the dynamic stress and electric field intensity around the circular inclusion are obtained.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109546"},"PeriodicalIF":2.9,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143592331","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
Breather and rogue wave solutions for the variable coefficient nonlinear Schrödinger equation on Jacobian elliptic function periodic backgrounds 雅各布椭圆函数周期背景上可变系数非线性薛定谔方程的呼吸波和流氓波解决方案
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-03-01 DOI: 10.1016/j.aml.2025.109524
Meng-Chu Wei, Xiao-Yong Wen
{"title":"Breather and rogue wave solutions for the variable coefficient nonlinear Schrödinger equation on Jacobian elliptic function periodic backgrounds","authors":"Meng-Chu Wei,&nbsp;Xiao-Yong Wen","doi":"10.1016/j.aml.2025.109524","DOIUrl":"10.1016/j.aml.2025.109524","url":null,"abstract":"<div><div>This study concentrates on exact solutions on the Jacobian elliptic function periodic background to the variable-coefficient nonlinear Schrödinger (vcNLS) equation. Through constructing the new eigenvalue solution for Lax pair and using the known Darboux transformation (DT) of vcNLS equation, the breather and rogue wave (RW) structures on Jacobian elliptic function backgrounds are revealed. By changing the variable coefficients in the equation, some novel localized wave structures are discussed graphically. The results presented in this letter will provide a valuable theoretical support for solving localized waves on the complicated seed background of variable coefficient nonlinear equations.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109524"},"PeriodicalIF":2.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143529759","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
Orthogonal block Kaczmarz inner-iteration preconditioned flexible GMRES method for large-scale linear systems
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-03-01 DOI: 10.1016/j.aml.2025.109529
Xin-Fang Zhang , Meng-Long Xiao , Zhuo-Heng He
{"title":"Orthogonal block Kaczmarz inner-iteration preconditioned flexible GMRES method for large-scale linear systems","authors":"Xin-Fang Zhang ,&nbsp;Meng-Long Xiao ,&nbsp;Zhuo-Heng He","doi":"10.1016/j.aml.2025.109529","DOIUrl":"10.1016/j.aml.2025.109529","url":null,"abstract":"<div><div>Kacamarz-type inner-iteration preconditioned flexible GMRES method, which was proposed by Du et al. (2021), is attractive for solving consistent linear systems. However, its inner iteration was only performed by several commonly used Kaczmarz-type methods, and required computing <span><math><mrow><mi>A</mi><msup><mrow><mi>A</mi></mrow><mrow><mi>T</mi></mrow></msup></mrow></math></span> in advance, which is unfavorable for big data problems. To overcome these difficulties, we first propose a simple orthogonal block Kaczmarz method, based on the orthogonal block idea without preconditioning, which converges much faster than the mentioned-above Kaczmarz-type solvers. We then derive a simple orthogonal block Kaczmarz inner-iteration preconditioned flexible GMRES method, based on the orthogonal block Kaczmarz inner-iteration as a preconditioner, which is appealing for large-scale linear systems. The convergence analysis of which is also established. Finally, we provide some numerical examples to illustrate the effectiveness of the proposed methods compared with some state-of-the-art Kaczmarz-type methods.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109529"},"PeriodicalIF":2.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551291","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 solutions for the system of a viscous two-fluid model
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-03-01 DOI: 10.1016/j.aml.2025.109530
Yan Liu, Wenjun Wang
{"title":"Global solutions for the system of a viscous two-fluid model","authors":"Yan Liu,&nbsp;Wenjun Wang","doi":"10.1016/j.aml.2025.109530","DOIUrl":"10.1016/j.aml.2025.109530","url":null,"abstract":"<div><div>In this paper, we consider a viscous compressible two-fluid model with a pressure law that depends on two variables. We establish the existence theory for the global solution of this system within the <span><math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mi>N</mi></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>-framework <span><math><mrow><mo>(</mo><mi>N</mi><mo>≥</mo><mn>2</mn><mo>)</mo></mrow></math></span>, assuming that the <span><math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>-norm of the initial perturbation is small. The energy method combined with the low-frequency and high-frequency decomposition is used to derive the decay of the solution and hence the global existence. As a byproduct, we obtain the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-<span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> convergence rates for the solution.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109530"},"PeriodicalIF":2.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551288","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 a nonautonomous nonlinear model for cell growth and division
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-03-01 DOI: 10.1016/j.aml.2025.109528
Qihua Huang, Jie Ou, Xiumei Deng
{"title":"On a nonautonomous nonlinear model for cell growth and division","authors":"Qihua Huang,&nbsp;Jie Ou,&nbsp;Xiumei Deng","doi":"10.1016/j.aml.2025.109528","DOIUrl":"10.1016/j.aml.2025.109528","url":null,"abstract":"<div><div>In this paper, we propose and analyze a nonautonomous, nonlinear size-structured population model that describes the growth and division of cells. By applying the monotone method based on a comparison principle, we establish the well-posedness of the model. We then investigate the long-term behavior of the solution using the upper–lower solution approach. Specifically, we derive conditions on the model parameters that determine the persistence or extinction of the cell population.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109528"},"PeriodicalIF":2.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551294","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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