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Nonlinear bound states with prescribed angular momentum in the mass supercritical regime 质量超临界状态下具有规定角动量的非线性束缚态
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2025-09-25 DOI: 10.1016/j.jde.2025.113796
Tianxiang Gou , Xiaoan Shen
{"title":"Nonlinear bound states with prescribed angular momentum in the mass supercritical regime","authors":"Tianxiang Gou ,&nbsp;Xiaoan Shen","doi":"10.1016/j.jde.2025.113796","DOIUrl":"10.1016/j.jde.2025.113796","url":null,"abstract":"<div><div>In this paper, we consider the existence, orbital stability/instability and regularity of bound state solutions to nonlinear Schrödinger equations with super-quadratic confinement in two and three spatial dimensions for the mass supercritical case. Such solutions, which are given by time-dependent rotations of a non-radially symmetric spatial profile, correspond to critical points of the underlying energy function restricted on the double constraints consisting of the mass and the angular momentum. The study exhibits new pictures for rotating Bose-Einstein condensates within the framework of Gross-Pitaevskii theory. It is proved that there exist two non-radial symmetric solutions, one of which is local minimizer and the other is mountain pass type critical point of the underlying energy function restricted on the constraints. Moreover, we derive conditions that guarantee that local minimizers are regular, the set of those is orbitally stable and mountain pass type solutions are strongly unstable. The results extend and complement the recent ones in <span><span>[17]</span></span>, where the consideration is undertaken in the mass subcritical case.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"453 ","pages":"Article 113796"},"PeriodicalIF":2.3,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145156708","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
Internal control of the transition kernel for stochastic lattice dynamics 随机晶格动力学转移核的内部控制
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2025-09-25 DOI: 10.1016/j.jde.2025.113798
Amirali Hannani , Minh-Nhat Phung , Minh-Binh Tran , Emmanuel Trélat
{"title":"Internal control of the transition kernel for stochastic lattice dynamics","authors":"Amirali Hannani ,&nbsp;Minh-Nhat Phung ,&nbsp;Minh-Binh Tran ,&nbsp;Emmanuel Trélat","doi":"10.1016/j.jde.2025.113798","DOIUrl":"10.1016/j.jde.2025.113798","url":null,"abstract":"<div><div>In <span><span>[4]</span></span>, we initiated the first study of control problems for kinetic equations arising from harmonic chains. Specifically, we developed impulsive and feedback control mechanisms for harmonic chains coupled with a point thermostat, effectively enabling control over the boundary conditions of the corresponding kinetic equations. However, the more intricate and fundamental challenge of internal control - namely, the design of control strategies that influence the collision operators within the kinetic framework - remained open.</div><div>In the present work, we address the internal control problem for stochastic lattice dynamics, with the objective of controlling the transition kernel of the limiting kinetic equation. A central innovation of our approach is the development of a novel geometric-combinatorial framework, which enables the systematic construction of control pathways within the microscopic dynamics. This methodology opens a new avenue for the internal control of kinetic equations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"453 ","pages":"Article 113798"},"PeriodicalIF":2.3,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145156709","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
Wave breaking criteria for a generalized Fornberg-Whitham equation 广义Fornberg-Whitham方程的破波准则
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2025-09-25 DOI: 10.1016/j.jde.2025.113795
Changtai Zhou, Shaoyong Lai
{"title":"Wave breaking criteria for a generalized Fornberg-Whitham equation","authors":"Changtai Zhou,&nbsp;Shaoyong Lai","doi":"10.1016/j.jde.2025.113795","DOIUrl":"10.1016/j.jde.2025.113795","url":null,"abstract":"<div><div>The blowup features for a generalized Fornberg-Whitham equation are investigated on the line. Using the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> conservation law and the method to construct Lyapunov functions, sufficient conditions ensuring that wave breaking occurs for the equation are provided. Under certain assumptions, our wave breaking results improve the wave breaking criteria in Wei (2023) <span><span>[25]</span></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"453 ","pages":"Article 113795"},"PeriodicalIF":2.3,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145156740","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
Smoothness of the inertial manifold via the spatial averaging principle 基于空间平均原理的惯性流形平滑
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2025-09-25 DOI: 10.1016/j.jde.2025.113790
Ziqi Niu , Xinhua Li , Chunyou Sun
{"title":"Smoothness of the inertial manifold via the spatial averaging principle","authors":"Ziqi Niu ,&nbsp;Xinhua Li ,&nbsp;Chunyou Sun","doi":"10.1016/j.jde.2025.113790","DOIUrl":"10.1016/j.jde.2025.113790","url":null,"abstract":"<div><div>This paper investigates the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>ε</mi></mrow></msup><msub><mrow><mo>|</mo></mrow><mrow><mo>{</mo><mi>n</mi><mo>≥</mo><mn>2</mn><mo>,</mo><mi>ε</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo><mo>}</mo></mrow></msub></math></span>-smoothness of the inertial manifold for an abstract semilinear parabolic equation. Compared with the known results, the required spectral gap condition has been relaxed by applying the principle of spatial averaging initially proposed by J. Mallet-Paret and G. Sell in 1988.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"453 ","pages":"Article 113790"},"PeriodicalIF":2.3,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145156710","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
Nonexistence of solutions to parabolic problems with a potential on weighted graphs 加权图上带势抛物型问题解的不存在性
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2025-09-24 DOI: 10.1016/j.jde.2025.113782
Dario D. Monticelli, Fabio Punzo, Jacopo Somaglia
{"title":"Nonexistence of solutions to parabolic problems with a potential on weighted graphs","authors":"Dario D. Monticelli,&nbsp;Fabio Punzo,&nbsp;Jacopo Somaglia","doi":"10.1016/j.jde.2025.113782","DOIUrl":"10.1016/j.jde.2025.113782","url":null,"abstract":"<div><div>We investigate nonexistence of nontrivial nonnegative solutions to a class of semilinear parabolic equations with a positive potential, posed on weighted graphs. Assuming an upper bound on the Laplacian of the distance and a suitable weighted space-time volume growth condition, we show that no global solutions exist. We also discuss the optimality of the hypotheses, thus recovering a critical exponent phenomenon of Fujita type.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"453 ","pages":"Article 113782"},"PeriodicalIF":2.3,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145120169","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
Stretching of polymers and turbulence: Fokker Planck equation, special stochastic scaling limit and stationary law 聚合物的拉伸与湍流：Fokker - Planck方程，特殊随机标度极限和平稳定律
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2025-09-24 DOI: 10.1016/j.jde.2025.113789
Franco Flandoli, Yassine Tahraoui
{"title":"Stretching of polymers and turbulence: Fokker Planck equation, special stochastic scaling limit and stationary law","authors":"Franco Flandoli,&nbsp;Yassine Tahraoui","doi":"10.1016/j.jde.2025.113789","DOIUrl":"10.1016/j.jde.2025.113789","url":null,"abstract":"<div><div>The aim of this work is understanding the stretching mechanism of stochastic models of turbulence acting on a simple model of dilute polymers. We consider a turbulent model that is white noise in time and activates frequencies in a shell <span><math><mi>N</mi><mo>≤</mo><mo>|</mo><mi>k</mi><mo>|</mo><mo>≤</mo><mn>2</mn><mi>N</mi></math></span> and investigate the scaling limit as <span><math><mi>N</mi><mo>→</mo><mo>∞</mo></math></span>, under suitable intensity assumption, such that the stretching term has a finite limit covariance. The polymer density equation, initially an SPDE, converges weakly to a limit deterministic equation with a new term. Stationary solutions can be computed and show power law decay in the polymer length.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"452 ","pages":"Article 113789"},"PeriodicalIF":2.3,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145120566","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
Wave equation with nonlinear damping and super-cubic nonlinearity 非线性阻尼和超三次非线性波动方程
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2025-09-24 DOI: 10.1016/j.jde.2025.113783
Cuncai Liu , Fengjuan Meng , Xiaoying Han , Chang Zhang
{"title":"Wave equation with nonlinear damping and super-cubic nonlinearity","authors":"Cuncai Liu ,&nbsp;Fengjuan Meng ,&nbsp;Xiaoying Han ,&nbsp;Chang Zhang","doi":"10.1016/j.jde.2025.113783","DOIUrl":"10.1016/j.jde.2025.113783","url":null,"abstract":"<div><div>This study investigates a semilinear wave equation characterized by nonlinear damping <span><math><mi>g</mi><mo>(</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></math></span> and nonlinearity <span><math><mi>f</mi><mo>(</mo><mi>u</mi><mo>)</mo></math></span>. First, the well-posedness of weak solutions across broader exponent ranges for <em>g</em> and <em>f</em> is established, by utilizing a priori space-time estimates. Moreover, the existence of a global attractor in the phase space <span><math><msubsup><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn></mrow></msubsup><mo>(</mo><mi>Ω</mi><mo>)</mo><mo>×</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span> is obtained. Furthermore, it is proved that this global attractor is regular, implying that it is a bounded subset of <span><math><mo>(</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>Ω</mi><mo>)</mo><mo>∩</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn></mrow></msubsup><mo>(</mo><mi>Ω</mi><mo>)</mo><mo>)</mo><mo>×</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn></mrow></msubsup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"452 ","pages":"Article 113783"},"PeriodicalIF":2.3,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145120568","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
Three-dimensional horseshoes near an unfolding of a Hopf-Hopf singularity Hopf-Hopf奇点展开附近的三维马蹄铁
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2025-09-24 DOI: 10.1016/j.jde.2025.113778
Santiago Ibáñez , Alexandre A. Rodrigues
{"title":"Three-dimensional horseshoes near an unfolding of a Hopf-Hopf singularity","authors":"Santiago Ibáñez ,&nbsp;Alexandre A. Rodrigues","doi":"10.1016/j.jde.2025.113778","DOIUrl":"10.1016/j.jde.2025.113778","url":null,"abstract":"<div><div>Motivated by a certain type of unfolding of a Hopf-Hopf singularity, we consider a one-parameter family <span><math><msub><mrow><mo>(</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>γ</mi><mo>≥</mo><mn>0</mn></mrow></msub></math></span> of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>–vector fields in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span> whose flows exhibit a heteroclinic cycle associated to two periodic solutions and a bifocus, all of them hyperbolic. It is formally proved that combining rotation with a generic condition concerning the transverse intersection between the three-dimensional invariant manifolds of the periodic solutions, all sets are highly distorted by the first return map and hyperbolic three-dimensional horseshoes emerge, accumulating on the network. Infinitely many linked horseshoes prompt the coexistence of infinitely many saddle-type invariant sets for all values of <span><math><mi>γ</mi><mo>≳</mo><mn>0</mn></math></span> belonging to the heteroclinic class of the two hyperbolic periodic solutions. We apply the results to a particular unfolding of the Hopf-Hopf singularity, the so-called <em>Gaspard-type unfolding</em>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"452 ","pages":"Article 113778"},"PeriodicalIF":2.3,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145156936","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 of weak solutions to a parabolic attraction-repulsion chemotaxis model in R3: The repulsive dominant case R3中抛物型吸引-排斥趋化性模型弱解的整体存在性：排斥性优势情况
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2025-09-24 DOI: 10.1016/j.jde.2025.113791
Chia-Yu Hsieh, Yuan Wang
{"title":"Global existence of weak solutions to a parabolic attraction-repulsion chemotaxis model in R3: The repulsive dominant case","authors":"Chia-Yu Hsieh,&nbsp;Yuan Wang","doi":"10.1016/j.jde.2025.113791","DOIUrl":"10.1016/j.jde.2025.113791","url":null,"abstract":"<div><div>We consider the Cauchy problem for a full parabolic attraction-repulsion chemotaxis model in three dimensions. Due to the combination of diffusion, aggregation and repulsion effects, solutions to the model may exist globally or blow up in finite time. It is natural to expect that solutions exist globally in time when the chemorepellent is dominant. However, the global existence is only known in two dimensions. In this work, we establish the global existence of weak solutions for the repulsive dominant case in three dimensions.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"452 ","pages":"Article 113791"},"PeriodicalIF":2.3,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145120567","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
Convergence towards discontinuous patterns for a degenerate reaction-diffusion system with a non-monotone term 具有非单调项的退化反应-扩散系统的不连续模式收敛性
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2025-09-23 DOI: 10.1016/j.jde.2025.113793
Guillaume Cantin
{"title":"Convergence towards discontinuous patterns for a degenerate reaction-diffusion system with a non-monotone term","authors":"Guillaume Cantin","doi":"10.1016/j.jde.2025.113793","DOIUrl":"10.1016/j.jde.2025.113793","url":null,"abstract":"<div><div>In this paper, we establish new results on the dynamics of a degenerate reaction-diffusion system with hysteresis. Our model determines the evolution of a biological system characterized by the interaction between a sedentary species and a diffusive species. It can be notably applied in forest ecology and in microbiology. We prove the existence of an infinite family of discontinuous stationary solutions using a generalized Mountain Pass Theorem, and analyze the continuity of this family, through an original method based on the convergence of generalized Clarke gradients. We show that the discontinuity interface of the heterogeneous patterns is very sensitive with respect to a variation of the initial condition. Furthermore, we prove a new theorem of convergence towards discontinuous patterns, which shows that the basin of attraction of each pattern contains a non-trivial set of initial conditions.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"453 ","pages":"Article 113793"},"PeriodicalIF":2.3,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145120170","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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