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The minimal periodic solutions for superquadratic autonomous Hamiltonian systems without the Palais-Smale condition 无 Palais-Smale 条件的超二次自洽哈密顿系统的最小周期解
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2024-09-12 DOI: 10.1016/j.jde.2024.09.005
Yuming Xiao , Gaosheng Zhu
{"title":"The minimal periodic solutions for superquadratic autonomous Hamiltonian systems without the Palais-Smale condition","authors":"Yuming Xiao ,&nbsp;Gaosheng Zhu","doi":"10.1016/j.jde.2024.09.005","DOIUrl":"10.1016/j.jde.2024.09.005","url":null,"abstract":"<div><p>In this paper, we prove the existence of periodic solutions with any prescribed minimal period <span><math><mi>T</mi><mo>&gt;</mo><mn>0</mn></math></span> for even second order Hamiltonian systems and convex first order Hamiltonian systems under the weak Nehari condition instead of Ambrosetti-Rabinowitz's. To this end, we shall develop the method of Nehari manifold to directly deal with a frequently occurring problem where the Nehari set is not a manifold.</p></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142171606","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
Invasion analysis on a predator-prey system with a variable habitat for predators in open advective environments 对开放平流环境中捕食者栖息地可变的捕食者-猎物系统的入侵分析
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2024-09-11 DOI: 10.1016/j.jde.2024.09.007
Baifeng Zhang , Xianning Liu , Yangjiang Wei
{"title":"Invasion analysis on a predator-prey system with a variable habitat for predators in open advective environments","authors":"Baifeng Zhang ,&nbsp;Xianning Liu ,&nbsp;Yangjiang Wei","doi":"10.1016/j.jde.2024.09.007","DOIUrl":"10.1016/j.jde.2024.09.007","url":null,"abstract":"<div><p>Community composition in aquatic environments is influenced by habitat conditions, such as location and size. We propose a system of reaction-diffusion-advection equations for a predator-prey model with variable predator habitat in open advective environments. We investigate the effects of the location and length of the predator's habitat on its invasion. Firstly, we show that the closer the predator's habitat is to the downstream, the easier the predator can invade when its habitat length is fixed. Secondly, we find that increment of the predator's habitat length facilitates its invasion when the upstream boundary of its habitat is fixed. However, increment of the predator's habitat length disadvantages its invasion when the downstream boundary of its habitat is fixed. Thirdly, we obtain the uniqueness of positive steady state when two species reside in different domains. Finally, we numerically analyze how the advection rates affect the populations persistence and spatial distributions of the populations. These findings may have important biological implications and applications on the invasion of predators in open advective environments.</p></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142169062","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
Uniform regularity and vanishing dissipation limit for the 3D magnetic Bénard equations in half space 半空间三维磁性贝纳德方程的均匀正则性和耗散消失极限
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2024-09-11 DOI: 10.1016/j.jde.2024.09.018
Jing Wang , Xueyi Zhang
{"title":"Uniform regularity and vanishing dissipation limit for the 3D magnetic Bénard equations in half space","authors":"Jing Wang ,&nbsp;Xueyi Zhang","doi":"10.1016/j.jde.2024.09.018","DOIUrl":"10.1016/j.jde.2024.09.018","url":null,"abstract":"<div><p>In this paper, we are concerned with the uniform regularity and zero dissipation limit of solutions to the initial boundary value problem of 3D incompressible magnetic Bénard equations in the half space, where the velocity field satisfies the no-slip boundary conditions, the magnetic field satisfies the perfect conducting boundary conditions, and the temperature satisfies either the zero Neumann or zero Dirichlet boundary condition. With the assumption that the magnetic field is transverse to the boundary, we establish the uniform regularity energy estimates of solutions as both viscosity and magnetic diffusion coefficients go to zero, which means there is no strong boundary layer under the no-slip boundary condition even the energy equation is included. Then the zero dissipation limit of solutions for this problem can be regarded as a direct consequence of these uniform regularity estimates by some compactness arguments.</p></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142169063","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
Rigidity of Lyapunov exponents for geodesic flows 大地流 Lyapunov 指数的刚性
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2024-09-11 DOI: 10.1016/j.jde.2024.09.004
Nestor Nina Zarate , Sergio Romaña
{"title":"Rigidity of Lyapunov exponents for geodesic flows","authors":"Nestor Nina Zarate ,&nbsp;Sergio Romaña","doi":"10.1016/j.jde.2024.09.004","DOIUrl":"10.1016/j.jde.2024.09.004","url":null,"abstract":"<div><p>In this paper, we study rigidity problems between Lyapunov exponents along periodic orbits and geometric structures. More specifically, we prove that for a surface <em>M</em> without focal points, if the value of the Lyapunov exponents is constant over all periodic orbits, then <em>M</em> is the flat 2-torus or a surface of constant negative curvature. We obtain the same result for the case of Anosov geodesic flow for surface, which generalizes C. Butler's result <span><span>[5]</span></span> in dimension two. Using completely different techniques, we also prove an extension of <span><span>[5]</span></span> to the finite volume case, where the value of the Lyapunov exponents along all periodic orbits is constant, being the maximum or minimum possible.</p></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142169059","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
Bifurcations of codimension 4 in a Leslie-type predator-prey model with Allee effects 具有阿利效应的莱斯利型捕食者-猎物模型中的第 4 维分岔
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2024-09-11 DOI: 10.1016/j.jde.2024.09.009
Jicai Huang , Min Lu , Chuang Xiang , Lan Zou
{"title":"Bifurcations of codimension 4 in a Leslie-type predator-prey model with Allee effects","authors":"Jicai Huang ,&nbsp;Min Lu ,&nbsp;Chuang Xiang ,&nbsp;Lan Zou","doi":"10.1016/j.jde.2024.09.009","DOIUrl":"10.1016/j.jde.2024.09.009","url":null,"abstract":"<div><p>In this paper, we explore a Leslie-type predator-prey model with simplified Holling IV functional response and Allee effects in prey. It is shown that the model can undergo a sequence of bifurcations including cusp, focus and saddle-node types nilpotent bifurcations of codimension four and a degenerate Hopf bifurcation of codimension up to four as the parameters vary. Our results indicate that Allee effects can induce richer dynamics and bifurcations, especially high sensitivities on both parameters and initial densities for coexistence and oscillations of both populations. Moreover, strong Allee effects (<span><math><mi>M</mi><mo>&gt;</mo><mn>0</mn></math></span>) (or ‘transitional Allee effects’ (<span><math><mi>M</mi><mo>=</mo><mn>0</mn></math></span>) with large predation rates) can cause the coextinction of both populations with some positive initial densities, while weak Allee effects (<span><math><mi>M</mi><mo>&lt;</mo><mn>0</mn></math></span>) (or transitional Allee effects with small predation rates) make both populations with positive initial densities persist. Finally, numerical simulations present some illustrations scarce in two-population models, such as the coexistence of three limit cycles and three positive equilibria.</p></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142169061","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
Hilbert expansion of Boltzmann equation with soft potentials and specular boundary condition in half-space 半空间软电势和镜面边界条件下玻尔兹曼方程的希尔伯特展开
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2024-09-11 DOI: 10.1016/j.jde.2024.09.001
Jing Ouyang , Yong Wang
{"title":"Hilbert expansion of Boltzmann equation with soft potentials and specular boundary condition in half-space","authors":"Jing Ouyang ,&nbsp;Yong Wang","doi":"10.1016/j.jde.2024.09.001","DOIUrl":"10.1016/j.jde.2024.09.001","url":null,"abstract":"<div><p>Boundary effects play an important role in the study of hydrodynamic limits in the Boltzmann theory. We justify rigorously the validity of the hydrodynamic limit from the Boltzmann equation of soft potentials to the compressible Euler equations by the Hilbert expansion with multi-scales. Specifically, the Boltzmann solutions are expanded into three parts: interior part, viscous boundary layer and Knudsen boundary layer. Due to the weak effect of collision frequency of soft potentials, new difficulty arises when tackling the existence of Knudsen layer solutions with space decay rate, which has been overcome under some constraint conditions and losing velocity weight arguments.</p></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142169060","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 the global well-posedness for the Fokas-Lenells equation on the line 论直线上 Fokas-Lenells 方程的全局好求解性
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2024-09-11 DOI: 10.1016/j.jde.2024.09.008
Qiaoyuan Cheng , Engui Fan , Manwai Yuen
{"title":"On the global well-posedness for the Fokas-Lenells equation on the line","authors":"Qiaoyuan Cheng ,&nbsp;Engui Fan ,&nbsp;Manwai Yuen","doi":"10.1016/j.jde.2024.09.008","DOIUrl":"10.1016/j.jde.2024.09.008","url":null,"abstract":"<div><p>We obtain the global well-posedness to the Cauchy problem of the Fokas-Lenells (FL) equation on the line without the small-norm assumption on initial data <span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>(</mo><mi>R</mi><mo>)</mo><mo>∩</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>R</mi><mo>)</mo></math></span>. Our main technical tool is the inverse scattering transform method based on the representation of a Riemann-Hilbert (RH) problem associated with the above Cauchy problem. The existence and the uniqueness of the RH problem is shown via a general vanishing lemma. By representing the solutions of the RH problem via the Cauchy integral protection and the reflection coefficients, the reconstruction formula is used to obtain a unique local solution of the FL equation. Further, the eigenfunctions and the reflection coefficients are shown Lipschitz continuous with respect to initial data, which provides a prior estimate of the solution to the FL equation. Based on the local solution and the uniformly prior estimate, we construct a unique global solution in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>(</mo><mi>R</mi><mo>)</mo><mo>∩</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>R</mi><mo>)</mo></math></span> to the FL equation.</p></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142169057","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 inverse problems in multi-population aggregation models 论多人口聚集模型中的逆问题
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2024-09-10 DOI: 10.1016/j.jde.2024.08.075
Yuhan Li, Hongyu Liu, Catharine W.K. Lo
{"title":"On inverse problems in multi-population aggregation models","authors":"Yuhan Li,&nbsp;Hongyu Liu,&nbsp;Catharine W.K. Lo","doi":"10.1016/j.jde.2024.08.075","DOIUrl":"10.1016/j.jde.2024.08.075","url":null,"abstract":"<div><p>This paper focuses on inverse problems arising in studying multi-population aggregations. The goal is to reconstruct the diffusion coefficient, advection coefficient, and interaction kernels of the aggregation system, which characterize the dynamics of different populations. In the theoretical analysis of the physical setup, it is crucial to ensure non-negativity of solutions. To address this, we employ the high-order variation method and introduce modifications to the systems. Additionally, we propose a novel approach called transformative asymptotic technique that enables the recovery of the diffusion coefficient preceding the Laplace operator, presenting a pioneering method for this type of problems. Through these techniques, we offer comprehensive insights into the unique identifiability aspect of inverse problems associated with multi-population aggregation models.</p></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142169058","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
Two dimensional NLS ground states with attractive Coulomb potential and point interaction 具有吸引力库仑势和点相互作用的二维 NLS 基态
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2024-09-10 DOI: 10.1016/j.jde.2024.08.076
Filippo Boni , Matteo Gallone
{"title":"Two dimensional NLS ground states with attractive Coulomb potential and point interaction","authors":"Filippo Boni ,&nbsp;Matteo Gallone","doi":"10.1016/j.jde.2024.08.076","DOIUrl":"10.1016/j.jde.2024.08.076","url":null,"abstract":"<div><p>We study the existence and the properties of ground states at fixed mass for a focusing nonlinear Schrödinger equation in dimension two with a point interaction, an attractive Coulomb potential and a nonlinearity of power type. We prove that for any negative value of the Coulomb charge, for any positive value of the mass and for any <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-subcritical power nonlinearity, such ground states exist and exhibit a logarithmic singularity where the interaction is placed. Moreover, up to multiplication by a phase factor, they are positive, radially symmetric and decreasing. An analogous result is obtained also for minimizers of the action restricted to the Nehari manifold, getting the existence also in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-critical and supercritical cases.</p></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142169056","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 free boundary inviscid model of flow-structure interaction 流动与结构相互作用的自由边界不粘性模型
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2024-09-09 DOI: 10.1016/j.jde.2024.08.045
Igor Kukavica , Amjad Tuffaha
{"title":"A free boundary inviscid model of flow-structure interaction","authors":"Igor Kukavica ,&nbsp;Amjad Tuffaha","doi":"10.1016/j.jde.2024.08.045","DOIUrl":"10.1016/j.jde.2024.08.045","url":null,"abstract":"<div><p>We obtain the local existence and uniqueness for a system describing interaction of an incompressible inviscid fluid, modeled by the Euler equations, and an elastic plate, represented by the fourth-order hyperbolic PDE. We provide a priori estimates for the existence with the optimal regularity <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>r</mi></mrow></msup></math></span>, for <span><math><mi>r</mi><mo>&gt;</mo><mn>2.5</mn></math></span>, on the fluid initial data and construct a unique solution of the system for initial data <span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mi>r</mi></mrow></msup></math></span> for <span><math><mi>r</mi><mo>≥</mo><mn>3</mn></math></span>. An important feature of the existence theorem is that the Taylor-Rayleigh instability does not occur. This is in contrast to the free-boundary Euler problem, where the stability condition on the initial pressure needs to be imposed.</p></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142158044","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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