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Liouville-type theorems for the stationary ideal compressible MHD equations 定态理想可压缩MHD方程的liouville型定理
IF 2.8 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-29 DOI: 10.1016/j.aml.2025.109694
Youseung Cho , Hyunjin In , Minsuk Yang
{"title":"Liouville-type theorems for the stationary ideal compressible MHD equations","authors":"Youseung Cho ,&nbsp;Hyunjin In ,&nbsp;Minsuk Yang","doi":"10.1016/j.aml.2025.109694","DOIUrl":"10.1016/j.aml.2025.109694","url":null,"abstract":"<div><div>We study Liouville-type theorems for the stationary ideal compressible magnetohydrodynamics (MHD) equations in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> for <span><math><mrow><mi>n</mi><mo>≥</mo><mn>1</mn></mrow></math></span>. In particular, we improve the theorems of Cai et al. (2024) (specifically Theorems 1.1 and 1.2). We remove symmetry assumptions such as axial symmetry without swirl and establish Liouville-type theorems under significantly weaker integrability conditions. We derive mean value identities and corresponding monotonicity properties to prove that smooth solutions satisfying a vanishing energy-type condition at infinity must be trivial. The results extend to lower-dimensional reduced models derived from the MHD system.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"172 ","pages":"Article 109694"},"PeriodicalIF":2.8,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144739593","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 spreading phenomenon of solutions for reaction–diffusion equations with fractional Laplacian 分数阶拉普拉斯反应扩散方程解的扩散现象
IF 2.8 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-28 DOI: 10.1016/j.aml.2025.109698
Luyi Ma , Hong-Tao Niu , Zhi-Cheng Wang
{"title":"The spreading phenomenon of solutions for reaction–diffusion equations with fractional Laplacian","authors":"Luyi Ma ,&nbsp;Hong-Tao Niu ,&nbsp;Zhi-Cheng Wang","doi":"10.1016/j.aml.2025.109698","DOIUrl":"10.1016/j.aml.2025.109698","url":null,"abstract":"<div><div>This paper is concerned with the Cauchy problem for the reaction–diffusion equations with fractional Laplacian. We showed that when the initial value is compactly supported and the support width is large enough, the solution for the reaction–diffusion equations with fractional Laplacian will spread to 1. In addition, the speed <span><math><mi>c</mi></math></span> of planar traveling wave front is also the spreading speed.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"172 ","pages":"Article 109698"},"PeriodicalIF":2.8,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144720897","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
Large-time behavior for compressible Navier–Stokes equations subject to large external potential forces in a three-dimensional bounded domain 三维有界区域中受大外力作用的可压缩Navier-Stokes方程的大时间行为
IF 2.8 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-28 DOI: 10.1016/j.aml.2025.109699
Lin Xu, Xin Zhong
{"title":"Large-time behavior for compressible Navier–Stokes equations subject to large external potential forces in a three-dimensional bounded domain","authors":"Lin Xu,&nbsp;Xin Zhong","doi":"10.1016/j.aml.2025.109699","DOIUrl":"10.1016/j.aml.2025.109699","url":null,"abstract":"<div><div>This paper investigates the large-time behavior for compressible Navier–Stokes equations subject to large external potential forces in a three-dimensional (3D) bounded domain with slip boundary conditions. Under the assumptions of small initial energy and a positive lower bound on the initial density, we prove that the density decays exponentially to the steady-state in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span>-norm. Moreover, we show that vacuum states persist when the initial density contains vacuum (even at a single point).</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"172 ","pages":"Article 109699"},"PeriodicalIF":2.8,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144720895","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
Acoustic eigenvalue analysis by singular boundary method with the block Sakurai–Sugiura method 基于块Sakurai-Sugiura方法的奇异边界法声学特征值分析
IF 2.8 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-24 DOI: 10.1016/j.aml.2025.109702
Weiwei Li, Chenchen Yang
{"title":"Acoustic eigenvalue analysis by singular boundary method with the block Sakurai–Sugiura method","authors":"Weiwei Li,&nbsp;Chenchen Yang","doi":"10.1016/j.aml.2025.109702","DOIUrl":"10.1016/j.aml.2025.109702","url":null,"abstract":"<div><div>This study presents a novel numerical solver for the nonlinear eigenvalue analysis of acoustic problems utilizing the singular boundary method (SBM). The proposed methodology integrates a contour integral technique referred as the block Sakurai-Sugiura (SS) method to effectively address the frequency-dependent nonlinearity inherent in SBM formulations. The Burton–Miller formulation is utilized to identify the fictitious eigenvalues associated with multiply-connected domains. Numerical experiments indicate that the developed eigensolver attains a high level of accuracy in eigenvalue extraction, with comparative analyses against analytical solutions affirming both its computational efficiency and robustness.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"172 ","pages":"Article 109702"},"PeriodicalIF":2.8,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144720896","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 new high-order compact CN-ADI scheme on graded meshes for three-dimensional nonlinear PIDEs with multiple weakly singular kernels 具有多个弱奇异核的三维非线性PIDEs的分级网格高阶紧致CN-ADI格式
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-24 DOI: 10.1016/j.aml.2025.109697
Tianyuan Liu , Haixiang Zhang , Song Wang
{"title":"A new high-order compact CN-ADI scheme on graded meshes for three-dimensional nonlinear PIDEs with multiple weakly singular kernels","authors":"Tianyuan Liu ,&nbsp;Haixiang Zhang ,&nbsp;Song Wang","doi":"10.1016/j.aml.2025.109697","DOIUrl":"10.1016/j.aml.2025.109697","url":null,"abstract":"<div><div>This study presents a novel compact Crank–Nicolson alternating direction implicit (CN-ADI) difference scheme tailored for three-dimensional (3D) nonlinear partial integro-differential equations (PIDEs) with multiple weakly singular kernels. The Riemann–Liouville (R-L) integral terms are discretized using the trapezoidal product integration (PI) rule, and the nonlinear term are approximated via second-order Taylor expansion. The time derivative is discretized using the CN formula, and the graded meshes are employed to address the weak singularity near <span><math><mrow><mi>t</mi><mo>=</mo><mn>0</mn></mrow></math></span>. The rigorous error estimates for the proposed scheme are derived, and comprehensive numerical experiments validate the theoretical results.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109697"},"PeriodicalIF":2.9,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144702986","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
New estimates for the mild solution to modified wave equation on the unbounded domain 无界区域上修正波动方程温和解的新估计
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-22 DOI: 10.1016/j.aml.2025.109668
Nguyen Huy Tuan , Bui Dai Nghia
{"title":"New estimates for the mild solution to modified wave equation on the unbounded domain","authors":"Nguyen Huy Tuan ,&nbsp;Bui Dai Nghia","doi":"10.1016/j.aml.2025.109668","DOIUrl":"10.1016/j.aml.2025.109668","url":null,"abstract":"<div><div>This paper studies the modified wave equation, Love equation, on the unbounded domain <span><math><mi>R</mi></math></span>. We prove that, given suitable initial data, there exists a unique mild solution that remains bounded in <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span>. Our approach uses a smooth cutoff function to split the Fourier integral into high- and low-frequency parts and incorporates a scaling factor to ensure convergence of the time integrals. New estimates for some kernels are introduced. We also show that, as a key parameter tends to zero, the solution of the modified wave equation converges to the solution of the classical wave equation. To the best of our knowledge, this is the first study of the modified wave equation (Love equation) in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span> setting, addressing a significant problem in the analysis of wave equations on unbounded domains.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109668"},"PeriodicalIF":2.9,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144687400","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
Exact analytical solution of the parabolic two-step model for nanoscale heat conduction 纳米尺度热传导抛物线两步模型的精确解析解
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-22 DOI: 10.1016/j.aml.2025.109693
A.S.N. Chairuca , A.J.A. Ramos , J.A.R. Nascimento , L.G.R. Miranda
{"title":"Exact analytical solution of the parabolic two-step model for nanoscale heat conduction","authors":"A.S.N. Chairuca ,&nbsp;A.J.A. Ramos ,&nbsp;J.A.R. Nascimento ,&nbsp;L.G.R. Miranda","doi":"10.1016/j.aml.2025.109693","DOIUrl":"10.1016/j.aml.2025.109693","url":null,"abstract":"<div><div>This work presents an analytical solution to the parabolic two-step model, widely used in modeling nanoscale heat conduction, especially in metallic materials subjected to ultrashort laser pulses. The model describes the thermal coupling between the electron gas and the crystal lattice through a system of coupled differential equations. The main contribution of the article is the derivation of an explicit solution using the technique of separation of variables and Fourier series, without the need to assume the <em>null initial velocity</em> (<strong>NIV</strong>) condition, which is often imposed in the literature. The analytical solution provides a rigorous description of the transient behavior of the temperatures in the electronic and lattice subsystems, revealing the presence of exponential decay modes. Additionally, computational simulations are carried out to illustrate the rapid thermal dissipation in the electronic subsystem, followed by a slower redistribution in the crystal lattice, behavior that is characteristic of electron–phonon coupling at the nanoscale.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109693"},"PeriodicalIF":2.9,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144711750","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
Preserving-periodic Riemannian descent model reduction of linear discrete-time periodic systems with isometric vector transport on product manifolds 积流形上具有等距矢量输运的线性离散周期系统的保周期黎曼下降模型约简
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-20 DOI: 10.1016/j.aml.2025.109692
Kang-Li Xu , Li-Hong Dong , Bin Wang , Zhen Li
{"title":"Preserving-periodic Riemannian descent model reduction of linear discrete-time periodic systems with isometric vector transport on product manifolds","authors":"Kang-Li Xu ,&nbsp;Li-Hong Dong ,&nbsp;Bin Wang ,&nbsp;Zhen Li","doi":"10.1016/j.aml.2025.109692","DOIUrl":"10.1016/j.aml.2025.109692","url":null,"abstract":"<div><div>In this paper, we propose a Riemannian descent model reduction iterative method for linear discrete-time periodic (LDTP) systems. The preserving-periodic <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> optimal problem for LDTP systems is posed on a product of Stiefel manifolds. The key feature of the proposed method is the use of the Riemannian geometry, including the orthonormal tangent bases, the intrinsic representation of tangent vectors, and the isometric vector transport by parallelization. By deriving the intrinsic representation of tangent vectors in orthonormal tangent bases, the vector transport by parallelization on the product manifold is given and then we present a Riemannian descent search direction in conjugate gradient scheme to construct the desired reduced systems. The main advantages of our method are that it not only preserves the periodic time-varying structure during the reduction process, but also guarantees the convergence to stationary points. Finally, a numerical example is tested to show that the proposed method has good convergence performance in constructing <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> optimal reduced systems.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109692"},"PeriodicalIF":2.9,"publicationDate":"2025-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144665018","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
Non-autonomous rational soliton bound states and dynamics in the nonlocal Gross–Pitaevskii equation with a PT-symmetric potential 具有[公式省略]对称势的非局部Gross-Pitaevskii方程中的非自治有理孤子束缚态和动力学
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-19 DOI: 10.1016/j.aml.2025.109691
Haotian Wang , Fenghua Qi , Wenjun Liu
{"title":"Non-autonomous rational soliton bound states and dynamics in the nonlocal Gross–Pitaevskii equation with a PT-symmetric potential","authors":"Haotian Wang ,&nbsp;Fenghua Qi ,&nbsp;Wenjun Liu","doi":"10.1016/j.aml.2025.109691","DOIUrl":"10.1016/j.aml.2025.109691","url":null,"abstract":"<div><div>This paper investigates an integrable Gross–Pitaevskii equation with nonlocal nonlinear effects, which consists of a nonlocal nonlinear Schrödinger equation adding an external potential function. The generalized Darboux transformation is used to solve this equation directly. We obtain rational solitons that exhibit the coexistence of dark and anti-dark solitons in bound states, and numerical simulations verify the correctness and robustness of these solutions. The influence of nonlocal effects and external potentials on the solutions of rational-type solitons is discussed. Results demonstrated that the dynamical behaviors of these solutions are novel and distinct from those of the local Gross–Pitaevskii equation and nonlocal nonlinear Schrödinger equation, providing some help and guidance for the realization of various soliton bound states in optical experiments.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109691"},"PeriodicalIF":2.9,"publicationDate":"2025-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144664997","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
Some discrete solitons and interaction dynamical behaviors for a PT-symmetric discrete nonlocal nonlinear Schrödinger equation pt对称离散非局部非线性Schrödinger方程的离散孤子及其相互作用动力学行为
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-07-17 DOI: 10.1016/j.aml.2025.109680
Jingwe Yu, Li Li, Fajunn Yu, Kai Cui
{"title":"Some discrete solitons and interaction dynamical behaviors for a PT-symmetric discrete nonlocal nonlinear Schrödinger equation","authors":"Jingwe Yu,&nbsp;Li Li,&nbsp;Fajunn Yu,&nbsp;Kai Cui","doi":"10.1016/j.aml.2025.109680","DOIUrl":"10.1016/j.aml.2025.109680","url":null,"abstract":"<div><div>At present, there have been many achievements on the study of integrable nonlocal nonlinear Schrödinger (NNLS) equation, which can enrich the mathematical structure of the NNLS equation by adding the discrete conditions. Ablowitz proposed a method to solve the nonlocal discrete Schrödinger equation under decaying boundary conditions by using the inverse scattering transformation. At this stage, there are few work of the discrete nonlocal nonlinear Schrödinger(DNNLS) equation with PT-symmetric. A detailed study of the DNNLS equation with PT-symmetric under fast decaying boundary conditions is carried out by using Darboux transformation method, which obtains the novel formulation of the soliton solution with the 2 × 2 Lax pairs, then some dynamical behaviors of the novel soliton solutions are analyzed by selecting different seed solutions and the wave parameters.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109680"},"PeriodicalIF":2.9,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144653093","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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