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Asymptotic behavior in time of solution for the cubic nonlinear Schrödinger equation on the tadpole graph 立方非线性薛定谔方程在蝌蚪图上求解的时间渐近行为
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2024-11-15 DOI: 10.1016/j.jde.2024.11.006
Jun-ichi Segata
{"title":"Asymptotic behavior in time of solution for the cubic nonlinear Schrödinger equation on the tadpole graph","authors":"Jun-ichi Segata","doi":"10.1016/j.jde.2024.11.006","DOIUrl":"10.1016/j.jde.2024.11.006","url":null,"abstract":"<div><div>The purpose of this paper is to study large time behavior of solution to the cubic nonlinear Schrödinger equation on the tadpole graph which is a ring attached to a semi-infinite line subject to the Kirchhoff conditions at the junction. Note that the cubic nonlinearity belongs borderline between short and long range scatterings on the whole line. We show that if the initial data has some symmetry on the graph which excludes the standing wave solutions, then the asymptotic behavior of solution to this equation is given by the solution to linear equation with logarithmic phase correction by the nonlinear effect.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"416 ","pages":"Pages 1977-1999"},"PeriodicalIF":2.4,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142652796","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
Complete continuity and Fréchet derivatives of nodes in potentials for one-dimensional p-Laplacian 一维 p 拉普拉斯电位节点的完全连续性和弗雷谢特导数
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2024-11-15 DOI: 10.1016/j.jde.2024.11.008
Jifeng Chu , Gang Meng , Feng Wang , Meirong Zhang
{"title":"Complete continuity and Fréchet derivatives of nodes in potentials for one-dimensional p-Laplacian","authors":"Jifeng Chu ,&nbsp;Gang Meng ,&nbsp;Feng Wang ,&nbsp;Meirong Zhang","doi":"10.1016/j.jde.2024.11.008","DOIUrl":"10.1016/j.jde.2024.11.008","url":null,"abstract":"<div><div>The aim of this paper is to study the dependence of all nodes on integrable potentials, for one-dimensional <em>p</em>-Laplacian with separated boundary conditions, including the complete continuity of nodes in potentials with the weak topology, and the continuous Fréchet differentiability of nodes in potentials. We present the precise formula for the Fréchet derivatives of nodes in potentials. These results are natural but nontrivial generalizations of those for Sturm-Liouville operators, with quite different proofs due to the nonlinearity of the <em>p</em>-Laplacian.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"416 ","pages":"Pages 1960-1976"},"PeriodicalIF":2.4,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142652795","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 dynamics and evolutionarily stable strategies in a two-species competition patch model 双物种竞争斑块模型中的全局动态和进化稳定策略
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2024-11-15 DOI: 10.1016/j.jde.2024.10.041
Jie Liu, Shanshan Chen
{"title":"Global dynamics and evolutionarily stable strategies in a two-species competition patch model","authors":"Jie Liu,&nbsp;Shanshan Chen","doi":"10.1016/j.jde.2024.10.041","DOIUrl":"10.1016/j.jde.2024.10.041","url":null,"abstract":"<div><div>In this paper, we consider a two-species competition patch model in advective heterogeneous environments, where the two species are ecologically identical except for their dispersal rates. It is shown that there exist two critical values such that the species with slower dispersal rate wins the competition if the drift rate is smaller than one critical value, whereas the species with faster dispersal rate is selected if the drift rate is larger than the other critical value. Moreover, treating one species as a resident species and the other one as a mutant species, and viewing dispersal rates as strategies, we show that the dispersal rate of the resident species can be an evolutionarily stable strategy for some intermediate drift rate between the above two critical values.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"416 ","pages":"Pages 2175-2220"},"PeriodicalIF":2.4,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142652916","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
Invariant measures of stochastic Maxwell equations and ergodic numerical approximations 随机麦克斯韦方程的不变量和遍历数值近似值
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2024-11-15 DOI: 10.1016/j.jde.2024.10.039
Chuchu Chen , Jialin Hong , Lihai Ji , Ge Liang
{"title":"Invariant measures of stochastic Maxwell equations and ergodic numerical approximations","authors":"Chuchu Chen ,&nbsp;Jialin Hong ,&nbsp;Lihai Ji ,&nbsp;Ge Liang","doi":"10.1016/j.jde.2024.10.039","DOIUrl":"10.1016/j.jde.2024.10.039","url":null,"abstract":"<div><div>This paper studies the existence and uniqueness of the invariant measure for a class of stochastic Maxwell equations and proposes a novel kind of ergodic numerical approximations to inherit the intrinsic properties. The key to proving the ergodicity lies in the uniform regularity estimates of the exact and numerical solutions with respect to time, which are established by analyzing some important physical quantities. By introducing an auxiliary process, we show that the mean-square convergence order of the discontinuous Galerkin full discretization is <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span> in the temporal direction and <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span> in the spatial direction, which provides the convergence order of the numerical invariant measure to the exact one in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-Wasserstein distance.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"416 ","pages":"Pages 1899-1959"},"PeriodicalIF":2.4,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142652794","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 stability of a system of viscous balance laws arising from chemotaxis with dynamic boundary flux 具有动态边界通量的趋化作用所产生的粘性平衡定律系统的全局稳定性
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2024-11-15 DOI: 10.1016/j.jde.2024.10.037
Yanni Zeng , Kun Zhao
{"title":"Global stability of a system of viscous balance laws arising from chemotaxis with dynamic boundary flux","authors":"Yanni Zeng ,&nbsp;Kun Zhao","doi":"10.1016/j.jde.2024.10.037","DOIUrl":"10.1016/j.jde.2024.10.037","url":null,"abstract":"<div><div>This paper considers the global dynamics of classical solutions to an initial-boundary value problem of the system of viscous balance laws arising from chemotaxis in one space dimension:<span><span><span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>−</mo><msub><mrow><mo>(</mo><mi>u</mi><mi>v</mi><mo>)</mo></mrow><mrow><mi>x</mi></mrow></msub><mo>=</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>x</mi><mi>x</mi></mrow></msub><mo>+</mo><mi>u</mi><mo>(</mo><mn>1</mn><mo>−</mo><mi>u</mi><mo>)</mo><mo>,</mo><mspace></mspace><mi>x</mi><mo>∈</mo><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>,</mo><mspace></mspace><mi>t</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>−</mo><msub><mrow><mo>(</mo><mi>u</mi><mo>+</mo><msup><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mi>x</mi></mrow></msub><mo>=</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>x</mi><mi>x</mi></mrow></msub><mo>,</mo><mspace></mspace><mi>x</mi><mo>∈</mo><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>,</mo><mspace></mspace><mi>t</mi><mo>&gt;</mo><mn>0</mn><mo>.</mo></math></span></span></span> The system of equations is supplemented with <em>time-dependent influx</em> boundary condition for <em>u</em> and homogeneous Dirichlet boundary condition for <em>v</em>. Under suitable assumptions on the dynamic boundary data, it is shown that classical solutions with generic initial data exist globally in time. Moreover, the solutions are shown to converge to the constant equilibrium <span><math><mo>(</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></span>, as <span><math><mi>t</mi><mo>→</mo><mo>∞</mo></math></span>. There is no smallness assumption on the initial data. This is the first rigorous mathematical study of the model subject to dynamic Neumann boundary condition, and generalizes previous works in content and technicality.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"416 ","pages":"Pages 2221-2254"},"PeriodicalIF":2.4,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142652915","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
Spatio-temporal dynamics of nonlocal dispersal systems in time-space periodic habitats 时空周期性栖息地非局部扩散系统的时空动力学
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2024-11-15 DOI: 10.1016/j.jde.2024.11.001
Wan-Tong Li , Ming-Zhen Xin , Xiao-Qiang Zhao
{"title":"Spatio-temporal dynamics of nonlocal dispersal systems in time-space periodic habitats","authors":"Wan-Tong Li ,&nbsp;Ming-Zhen Xin ,&nbsp;Xiao-Qiang Zhao","doi":"10.1016/j.jde.2024.11.001","DOIUrl":"10.1016/j.jde.2024.11.001","url":null,"abstract":"<div><div>This paper is concerned with the spatio-temporal dynamics of nonlocal dispersal systems with monostable and time-space periodic nonlinearity. Firstly, when the dispersal kernels are all light-tailed, we obtain the existence and variational characterization of the linear spreading speed; while the accelerated propagation happens if one species has a long-tailed dispersal kernel, and the accelerated spreading rate can be determined by the principle eigenvalue of the linearized system and the tail of the maximum of kernels. Secondly, we establish the existence and non-existence of traveling waves and semi-transition-waves in cooperative case and non-cooperative, respectively. Lastly, we apply these analytic results to a man-environment-man model and conduct some numerical simulations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"416 ","pages":"Pages 2000-2042"},"PeriodicalIF":2.4,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142652797","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
Continuity estimates for the gradient of solutions to the Monge-Ampère equation with natural boundary condition 带自然边界条件的蒙日-安培方程解的梯度连续性估计
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2024-11-15 DOI: 10.1016/j.jde.2024.11.005
Huaiyu Jian, Ruixuan Zhu
{"title":"Continuity estimates for the gradient of solutions to the Monge-Ampère equation with natural boundary condition","authors":"Huaiyu Jian,&nbsp;Ruixuan Zhu","doi":"10.1016/j.jde.2024.11.005","DOIUrl":"10.1016/j.jde.2024.11.005","url":null,"abstract":"<div><div>We study the first derivative estimates for solutions to Monge-Ampère equations in terms of modulus of continuity. As a result, we establish the optimal global log-Lipschitz continuity for the gradient of solutions to the Monge-Ampère equation with natural boundary condition.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"416 ","pages":"Pages 2065-2084"},"PeriodicalIF":2.4,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142652799","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 existence and boundedness of solutions to a fully parabolic chemotaxis system with indirect signal production in R4 R4 中具有间接信号产生的全抛物线趋化系统解的全局存在性和有界性
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2024-11-15 DOI: 10.1016/j.jde.2024.10.035
Tatsuya Hosono , Philippe Laurençot
{"title":"Global existence and boundedness of solutions to a fully parabolic chemotaxis system with indirect signal production in R4","authors":"Tatsuya Hosono ,&nbsp;Philippe Laurençot","doi":"10.1016/j.jde.2024.10.035","DOIUrl":"10.1016/j.jde.2024.10.035","url":null,"abstract":"<div><div>Global existence and boundedness of solutions to the Cauchy problem for the four dimensional fully parabolic chemotaxis system with indirect signal production are studied. We prove that solutions with initial mass below <span><math><msup><mrow><mo>(</mo><mn>8</mn><mi>π</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span> exist globally in time. This value <span><math><msup><mrow><mo>(</mo><mn>8</mn><mi>π</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span> is known as the four dimensional threshold value of the initial mass determining whether blow-up of solutions occurs or not. Furthermore, some condition on the initial mass guaranteeing that the solution remains uniformly bounded is also obtained.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"416 ","pages":"Pages 2085-2133"},"PeriodicalIF":2.4,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142652800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solving Barcilon's inverse problems by the method of spectral mappings 用谱映射法解决巴西隆逆问题
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2024-11-14 DOI: 10.1016/j.jde.2024.10.044
Ai-Wei Guan , Chuan-Fu Yang , Natalia P. Bondarenko
{"title":"Solving Barcilon's inverse problems by the method of spectral mappings","authors":"Ai-Wei Guan ,&nbsp;Chuan-Fu Yang ,&nbsp;Natalia P. Bondarenko","doi":"10.1016/j.jde.2024.10.044","DOIUrl":"10.1016/j.jde.2024.10.044","url":null,"abstract":"<div><div>In this paper, we consider Barcilon's inverse problem, which consists in the recovery of the fourth-order differential operator from three spectra. The relationship of Barcilon's three spectra with the Weyl-Yurko matrix is obtained. Moreover, the uniqueness theorem for the inverse problem solution is proved by developing the ideas of the method of spectral mappings. Our approach allows us to obtain the result for the general case of complex-valued distributional coefficients. In the future, the methods and the results of this paper can be generalized to differential operators of orders greater than 4 and used for further development of the inverse problem theory for higher-order differential operators.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"416 ","pages":"Pages 1881-1898"},"PeriodicalIF":2.4,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142652793","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 bilinear restriction estimate for Schrödinger equations on 2D waveguide 关于二维波导上薛定谔方程的双线性限制估计
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2024-11-14 DOI: 10.1016/j.jde.2024.11.003
Yangkendi Deng
{"title":"On a bilinear restriction estimate for Schrödinger equations on 2D waveguide","authors":"Yangkendi Deng","doi":"10.1016/j.jde.2024.11.003","DOIUrl":"10.1016/j.jde.2024.11.003","url":null,"abstract":"<div><div>In this article, we prove a bilinear estimate for Schrödinger equations on 2d waveguide, <span><math><mi>R</mi><mo>×</mo><mi>T</mi></math></span>. We hope it may be of use in the further study of concentration compactness for cubic NLS on <span><math><mi>R</mi><mo>×</mo><mi>T</mi></math></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"416 ","pages":"Pages 1825-1836"},"PeriodicalIF":2.4,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142652790","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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