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Modelling intermediate internal waves with currents and variable bottom 模拟具有电流和可变底的中间内波
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-07-02 DOI: 10.1016/j.nonrwa.2025.104451
Rossen Ivanov, Lyudmila Ivanova
{"title":"Modelling intermediate internal waves with currents and variable bottom","authors":"Rossen Ivanov,&nbsp;Lyudmila Ivanova","doi":"10.1016/j.nonrwa.2025.104451","DOIUrl":"10.1016/j.nonrwa.2025.104451","url":null,"abstract":"<div><div>A model for internal interfacial waves between two layers of fluid in the presence of current and variable bottom is studied in the flat-surface approximation. Fluids are assumed to be incompressible and inviscid. Another assumption is that the upper layer is considerably deeper with a lower density than the lower layer. The fluid dynamics is presented in Hamiltonian form with appropriate Dirichlet–Neumann operators for the two fluid domains, and the depth-dependent current is taken into account. The well known integrable Intermediate Long Wave Equation (ILWE) is derived as an asymptotic internal waves model in the case of flat bottom. For a non-flat bottom the ILWE is with variable coefficients. Two limits of the ILWE lead to the integrable Benjamin–Ono and Korteweg-de Vries equations. Higher-order ILWE is obtained as well.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104451"},"PeriodicalIF":1.8,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144535728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 concept of instability and spatial patterns 不稳定性和空间格局的新概念
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-07-01 DOI: 10.1016/j.nonrwa.2025.104445
Milan Kučera , Václav Klika , Martin Fencl , Jan Eisner
{"title":"A new concept of instability and spatial patterns","authors":"Milan Kučera ,&nbsp;Václav Klika ,&nbsp;Martin Fencl ,&nbsp;Jan Eisner","doi":"10.1016/j.nonrwa.2025.104445","DOIUrl":"10.1016/j.nonrwa.2025.104445","url":null,"abstract":"<div><div>Non-standard notions of instability and spatial patterns are introduced and their robustness is proved. In fact, these notions correspond to what is really usually done in numerical computations or in a laboratory. Situations are described when our patterns evolve due to the newly introduced instability of the basic homogeneous steady state even if it is stable and even if heterogeneous stationary solutions do not exist.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104445"},"PeriodicalIF":1.8,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144518279","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Positive solutions of semipositone singular three-points boundary value problems for nonlinear fractional differential equations 非线性分数阶微分方程半正数奇异三点边值问题的正解
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-06-28 DOI: 10.1016/j.nonrwa.2025.104425
Xueyan Zhang , Zhaocai Hao , Martin Bohner
{"title":"Positive solutions of semipositone singular three-points boundary value problems for nonlinear fractional differential equations","authors":"Xueyan Zhang ,&nbsp;Zhaocai Hao ,&nbsp;Martin Bohner","doi":"10.1016/j.nonrwa.2025.104425","DOIUrl":"10.1016/j.nonrwa.2025.104425","url":null,"abstract":"<div><div>This study introduces the existence of one positive solution for a specific category of semipositive singular three-point boundary value problems associated with Caputo fractional differential equations. The proof relies on the application of the Guo–Krasnosel’skii fixed point theorem. In the end, we provide an illustrative example.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104425"},"PeriodicalIF":1.8,"publicationDate":"2025-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144501992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Dynamic contact of a beam–rod system with Signorini typed contact conditions and thermal effects 具有sigorini型接触条件和热效应的梁杆系统的动态接触
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-06-27 DOI: 10.1016/j.nonrwa.2025.104440
Sangmin Chun , Jeongho Ahn
{"title":"Dynamic contact of a beam–rod system with Signorini typed contact conditions and thermal effects","authors":"Sangmin Chun ,&nbsp;Jeongho Ahn","doi":"10.1016/j.nonrwa.2025.104440","DOIUrl":"10.1016/j.nonrwa.2025.104440","url":null,"abstract":"<div><div>This paper provides mathematical and numerical analyses for a beam–rod system with thermal effects. Its motion is described by a partial differential equation system with Signorini typed contact conditions. These conditions that cause a nonlinear model are interpreted as complementarity conditions (CCs) with a convolution. In particular, the convolution plays a role in incorporating a thermal effect of the surface of a rigid obstacle, which inspires us to investigate possibilities of proving conservation of energy under some assumptions. We employ the one-step-<span><math><mi>θ</mi></math></span> schemes to show that numerical trajectories for a variational formulation and the CCs are convergent. Additionally, an alternative approach supports the convergence results which are proved through the time discretizations. Finite element methods are combined with time discretization techniques to propose the fully discrete numerical schemes. Numerical stability is validated and simulations with selected data are presented as well.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104440"},"PeriodicalIF":1.8,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144490039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Comparison results for the fractional heat equation with a singular lower order term 具有低阶奇异项的分数阶热方程的比较结果
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-06-27 DOI: 10.1016/j.nonrwa.2025.104434
Barbara Brandolini , Ida de Bonis , Vincenzo Ferone , Bruno Volzone
{"title":"Comparison results for the fractional heat equation with a singular lower order term","authors":"Barbara Brandolini ,&nbsp;Ida de Bonis ,&nbsp;Vincenzo Ferone ,&nbsp;Bruno Volzone","doi":"10.1016/j.nonrwa.2025.104434","DOIUrl":"10.1016/j.nonrwa.2025.104434","url":null,"abstract":"<div><div>We provide symmetrization results in the form of mass concentration comparisons for fractional singular parabolic equations in infinite cylinders of the type <span><math><mrow><mi>Ω</mi><mo>×</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>)</mo></mrow></mrow></math></span>, where <span><math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></math></span> (<span><math><mrow><mi>N</mi><mo>≥</mo><mn>2</mn></mrow></math></span>) is a bounded, open set with Lipschitz boundary, and <span><math><mrow><mi>T</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>. The fundamental ingredients of the proof are an implicit time discretization procedure and a max/min argument, previously applied to nonlocal elliptic problems in the recent paper Brandolini et al. (2023).</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104434"},"PeriodicalIF":1.8,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144501963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Sobolev stability of hydrostatic ideal MHD equations in a thin domain 薄域中流体静力理想MHD方程的Sobolev稳定性
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-06-27 DOI: 10.1016/j.nonrwa.2025.104448
Tianyuan Yu
{"title":"Sobolev stability of hydrostatic ideal MHD equations in a thin domain","authors":"Tianyuan Yu","doi":"10.1016/j.nonrwa.2025.104448","DOIUrl":"10.1016/j.nonrwa.2025.104448","url":null,"abstract":"<div><div>In this paper, we study the two-dimensional ideal MHD equations in a thin domain. When the initial data is assumed to be a small perturbation of a positive background magnetic field, we prove the well-posedness of the re-scaled ideal MHD equations. Then we justify the limit from the re-scaled ideal MHD equations to the hydrostatic ideal MHD equations and obtain the precise convergence rate in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104448"},"PeriodicalIF":1.8,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144501964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Dynamics of a pest-natural enemy model with natural enemy periodic migration described by time delay 用时滞描述天敌周期性迁移的害虫-天敌模型动力学
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-06-27 DOI: 10.1016/j.nonrwa.2025.104454
Jianjun Jiao , Yunpeng Xiao
{"title":"Dynamics of a pest-natural enemy model with natural enemy periodic migration described by time delay","authors":"Jianjun Jiao ,&nbsp;Yunpeng Xiao","doi":"10.1016/j.nonrwa.2025.104454","DOIUrl":"10.1016/j.nonrwa.2025.104454","url":null,"abstract":"<div><div>In this work, we present a pest-natural enemy model with natural enemy periodic migration described by time delay. The globally attractive conditions for pest-elimination periodic solution <span><math><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>,</mo><mover><mrow><mi>P</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><mo>˜</mo></mrow></mover><mo>)</mo></mrow></math></span> of model <span><math><mrow><mo>(</mo><mn>2</mn><mo>.</mo><mn>1</mn><mo>)</mo></mrow></math></span> are acquired by methods of mathematical analysis. Permanent conditions of model <span><math><mrow><mo>(</mo><mn>2</mn><mo>.</mo><mn>1</mn><mo>)</mo></mrow></math></span> are also provided. Computer-assisted techniques are used to simulate the dynamical behaviors of model <span><math><mrow><mrow><mo>(</mo><mn>2</mn><mo>.</mo><mn>1</mn><mo>)</mo></mrow><mo>.</mo></mrow></math></span> Furthermore, Systematic sensitivity analysis of parameters are inserted to describe the dynamic interactions between pests and their natural enemies. Our results are more closer to pest management with periodic migration and enrich theories of integrated pest management.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104454"},"PeriodicalIF":1.8,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144490041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Local-in-time well-posedness for a magnetohydrodynamical model with intrinsic magnetisation 具有本征磁化的磁流体动力学模型的局部时间适定性
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-06-27 DOI: 10.1016/j.nonrwa.2025.104446
Noah Vinod, Thanh Tran
{"title":"Local-in-time well-posedness for a magnetohydrodynamical model with intrinsic magnetisation","authors":"Noah Vinod,&nbsp;Thanh Tran","doi":"10.1016/j.nonrwa.2025.104446","DOIUrl":"10.1016/j.nonrwa.2025.104446","url":null,"abstract":"<div><div>Ferromagnetic magnetohydrodynamics concerns the study of conducting fluids with intrinsic magnetisation under the influence of a magnetic field. It is a generalisation of the magnetohydrodynamical equations and takes into account the dynamics of the magnetisation of a fluid. First proposed by Lingam (2015), the usual equations of magnetohydrodynamics, namely the Navier–Stokes equation and the induction equation, are coupled with the Landau–Lifshitz–Gilbert equation. In this paper, the local-in-time existence, uniqueness and regularity of strong solutions to this system are discussed.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104446"},"PeriodicalIF":1.8,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144490040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Analysis and finite element solution of a Navier–Stokes hemivariational inequality for incompressible fluid flows with damping 含阻尼不可压缩流体流动的Navier-Stokes半变分不等式分析及有限元解
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-06-26 DOI: 10.1016/j.nonrwa.2025.104439
Wensi Wang , Xiaoliang Cheng , Weimin Han
{"title":"Analysis and finite element solution of a Navier–Stokes hemivariational inequality for incompressible fluid flows with damping","authors":"Wensi Wang ,&nbsp;Xiaoliang Cheng ,&nbsp;Weimin Han","doi":"10.1016/j.nonrwa.2025.104439","DOIUrl":"10.1016/j.nonrwa.2025.104439","url":null,"abstract":"<div><div>This paper provides a well-posedness analysis and a mixed finite element method for a hemivariational inequality of the stationary Navier–Stokes equations with a nonlinear damping term. The Navier–Stokes hemivariational inequality describes a steady incompressible fluid flow subject to a nonsmooth slip boundary condition of friction type. The well-posedness of the Navier–Stokes hemivariational inequality is established by constructing two auxiliary problems and applying Banach fixed point arguments twice. Mixed finite element methods are introduced to solve the problem, and error estimates for the solutions are derived. The error estimates are of optimal order for low-order mixed element pairs under suitable solution regularity assumptions. An efficient iterative algorithm is presented, and numerical results are provided to verify the theoretical analysis.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104439"},"PeriodicalIF":1.8,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144480883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Simultaneous stable determination of quasilinear terms for parabolic equations 抛物型方程拟线性项的同时稳定确定
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-06-25 DOI: 10.1016/j.nonrwa.2025.104442
Jason Choy , Yavar Kian
{"title":"Simultaneous stable determination of quasilinear terms for parabolic equations","authors":"Jason Choy ,&nbsp;Yavar Kian","doi":"10.1016/j.nonrwa.2025.104442","DOIUrl":"10.1016/j.nonrwa.2025.104442","url":null,"abstract":"<div><div>In this work, we consider the inverse problem of simultaneously recovering two classes of quasilinear terms appearing in a parabolic equation from boundary measurements. It is motivated by several industrial and scientific applications, including the problems of heat conduction and population dynamics, and we study the issue of stability. More precisely, we derive simultaneous Lipschitz and Hölder stability estimates for two separate classes of quasilinear terms. The analysis combines different arguments including the linearization technique with a novel construction of singular solutions and properties of solutions of parabolic equations with nonsmooth boundary conditions. These stability results may be useful for deriving the convergence rate of numerical reconstruction schemes.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104442"},"PeriodicalIF":1.8,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144472399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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