{"title":"Large-time behavior for compressible Navier–Stokes equations subject to large external potential forces in a three-dimensional bounded domain","authors":"Lin Xu, 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}
{"title":"Acoustic eigenvalue analysis by singular boundary method with the block Sakurai–Sugiura method","authors":"Weiwei Li, 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}
{"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 , Haixiang Zhang , 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}
{"title":"New estimates for the mild solution to modified wave equation on the unbounded domain","authors":"Nguyen Huy Tuan , 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}
{"title":"Exact analytical solution of the parabolic two-step model for nanoscale heat conduction","authors":"A.S.N. Chairuca , A.J.A. Ramos , J.A.R. Nascimento , 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}
{"title":"Preserving-periodic Riemannian descent model reduction of linear discrete-time periodic systems with isometric vector transport on product manifolds","authors":"Kang-Li Xu , Li-Hong Dong , Bin Wang , 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}
{"title":"Non-autonomous rational soliton bound states and dynamics in the nonlocal Gross–Pitaevskii equation with a PT-symmetric potential","authors":"Haotian Wang , Fenghua Qi , 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}
{"title":"Some discrete solitons and interaction dynamical behaviors for a PT-symmetric discrete nonlocal nonlinear Schrödinger equation","authors":"Jingwe Yu, Li Li, Fajunn Yu, 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}
{"title":"Bilinearization, solitons and modulational instability for a variable-coefficient nonlocal Hirota equation","authors":"Hao-Dong Liu, Bo Tian","doi":"10.1016/j.aml.2025.109688","DOIUrl":"10.1016/j.aml.2025.109688","url":null,"abstract":"<div><div>Hirota-type equations have been used to model certain nonlinear waves in the nonlinear optical fibers. In this paper, a variable-coefficient nonlocal Hirota equation is investigated: Via the improved Hirota method, we obtain the bilinear forms and soliton solutions; The asymptotic analysis is discussed; We also study the modulational instability.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"172 ","pages":"Article 109688"},"PeriodicalIF":2.8,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144665001","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 a sharp mixed Lebesgue upper bound for solutions to the defocusing nonlinear Schrödinger equation in dimension two","authors":"Vo Van Au","doi":"10.1016/j.aml.2025.109686","DOIUrl":"10.1016/j.aml.2025.109686","url":null,"abstract":"<div><div>In the unbounded two-dimensional domain, we study a class of nonlinear Schrödinger equations with a smooth power-type nonlinearity. We establish a novel global-in-time estimate that yields a sharp upper bound in the mixed Lebesgue space <span><math><mrow><msubsup><mrow><mi>L</mi></mrow><mrow><mi>t</mi></mrow><mrow><mn>4</mn></mrow></msubsup><msubsup><mrow><mi>L</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>8</mn></mrow></msubsup></mrow></math></span>. This work is motivated by the author’s previous results on the nonlinear Schrödinger equation, as well as by the influential work of Killip, Tao, and Visan (2009).</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109686"},"PeriodicalIF":2.9,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144663219","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}