{"title":"Relative sequence entropy for amenable group actions","authors":"Chunlin Liu , Changlin Wang , Weisheng Wu","doi":"10.1016/j.jde.2025.113582","DOIUrl":"10.1016/j.jde.2025.113582","url":null,"abstract":"<div><div>We introduce the concept of relative sequence entropy for amenable group actions and explore the interplay between relative sequence entropy and Kronecker algebras for amenable group actions, and rigid algebras for abelian group actions. Our investigation extends to the application of relative sequence entropy in various mixing concepts within both measure-theoretic and topological systems. Additionally, we refine the notion of relative sequence entropy by introducing the concept of relative sequence entropy pairs for amenable group actions.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"445 ","pages":"Article 113582"},"PeriodicalIF":2.4,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144517455","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":"Dynamics of a wave equation with memory and Hardy type potentials","authors":"Miaomiao Guo , Bo You , Tomás Caraballo","doi":"10.1016/j.jde.2025.113580","DOIUrl":"10.1016/j.jde.2025.113580","url":null,"abstract":"<div><div>This paper is concerned with the well-posedness and long-time dynamics for a wave equation with memory and Hardy type potentials. It is first proved the existence and uniqueness of weak solutions based on the Faedo-Galerkin approximation for <span><math><mn>0</mn><mo>≤</mo><mi>λ</mi><mo>≤</mo><mo>(</mo><mn>1</mn><mo>−</mo><msub><mrow><mi>δ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo><msup><mrow><mi>λ</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>. Moreover, the existence of a global attractor with finite fractal dimension is shown by establishing a quasi-stability inequality. Furthermore, we also establish the asymptotic regularity of the weak solution outside arbitrarily small neighborhoods of the origin. Finally, the upper semicontinuity of attractors is established when the parameter <em>λ</em> goes to <span><math><msup><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msup></math></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"444 ","pages":"Article 113580"},"PeriodicalIF":2.4,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144517150","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":"Quantitative analysis of elastic field in presence of three dimensional nanorod","authors":"Wanjing Tang , Youjun Deng , Xiaoping Fang","doi":"10.1016/j.jde.2025.113591","DOIUrl":"10.1016/j.jde.2025.113591","url":null,"abstract":"<div><div>In this paper, we investigate the perturbation of the elastic field in the context of a three dimensional straight nanorod. We obtain an exact asymptotic formula for the perturbation field by performing a detailed asymptotic analysis of the Neumann-Poincaré operator associated with this anisotropic geometry, which clearly shows the field accumulation near the high curvature points. Additionally, it is shown that all the eigenvalues of the related Neumann-Poincaré for a disk belong to the eigenmodes of three dimensional straight nanorod.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"445 ","pages":"Article 113591"},"PeriodicalIF":2.4,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144517453","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}
Francisco Alegría , Gong Chen , Claudio Muñoz , Felipe Poblete , Benjamín Tardy
{"title":"On uniqueness of KP soliton structures","authors":"Francisco Alegría , Gong Chen , Claudio Muñoz , Felipe Poblete , Benjamín Tardy","doi":"10.1016/j.jde.2025.113569","DOIUrl":"10.1016/j.jde.2025.113569","url":null,"abstract":"<div><div>We consider the Kadomtsev-Petviashvili II (KP) model placed in <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>×</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msubsup></math></span>, in the case of smooth data that are not necessarily in a Sobolev space. In this paper, the subclass of smooth solutions we study is of “soliton type”, characterized by a phase <span><math><mi>Θ</mi><mo>=</mo><mi>Θ</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></math></span> and a unidimensional profile <em>F</em>. In particular, every classical KP soliton and multi-soliton falls into this category with suitable Θ and <em>F</em>. We establish concrete characterizations of KP solitons by means of a natural set of nonlinear differential equations and inclusions of functionals of Wronskian, Airy and Heat types, among others. These functional equations only depend on the new variables Θ and <em>F</em>. A distinct characteristic of this set of functionals is its special and rigid structure tailored to the considered soliton. By analyzing Θ and <em>F</em>, we establish the uniqueness of line-solitons, multi-solitons, and other degenerate solutions among a large class of KP solutions. Our results are also valid for other 2D dispersive models such as the quadratic and cubic Zakharov-Kuznetsov equations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"445 ","pages":"Article 113569"},"PeriodicalIF":2.4,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144490404","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":"Asymptotic behavior of small solutions to a 2-component system of cubic nonlinear Schrödinger equations in one space dimension","authors":"Yuji Sagawa","doi":"10.1016/j.jde.2025.113576","DOIUrl":"10.1016/j.jde.2025.113576","url":null,"abstract":"<div><div>In this manuscript we specify asymptotic behavior of small solutions to initial value problem for a 2-component system of cubic nonlinear Schrödinger equations in one dimensional Euclidean space. As a consequence, the solution behaves like a free solution as <span><math><mi>t</mi><mo>→</mo><mo>+</mo><mo>∞</mo></math></span>. Moreover, a non-decay result for the solution is derived, which is non-trivial in terms of the long range scattering.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"444 ","pages":"Article 113576"},"PeriodicalIF":2.4,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144490448","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":"Determining Lorentzian manifold from non-linear wave observation at a single point","authors":"Medet Nursultanov , Lauri Oksanen , Leo Tzou","doi":"10.1016/j.jde.2025.113563","DOIUrl":"10.1016/j.jde.2025.113563","url":null,"abstract":"<div><div>We consider an inverse problem for a non-linear hyperbolic equation. We show that the conformal structure of a Lorentzian manifold can be determined by the source-to-solution map evaluated along a single timelike curve. We use the microlocal analysis of non-linear wave interaction.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"444 ","pages":"Article 113563"},"PeriodicalIF":2.4,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144490506","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}
Claudianor O. Alves , Paulo Cesar Carrião , André Vicente
{"title":"Stability and blow-up result for a class of a generalized Klein-Gordon equation","authors":"Claudianor O. Alves , Paulo Cesar Carrião , André Vicente","doi":"10.1016/j.jde.2025.113590","DOIUrl":"10.1016/j.jde.2025.113590","url":null,"abstract":"<div><div>In this paper we prove the existence of solution to a generalized Klein-Gordon equation with damping and source terms. The space derivative part of the main operator is described by a pseudo-differential operator given by <span><math><mo>−</mo><mi>Δ</mi><mi>exp</mi><mo></mo><mo>(</mo><mo>−</mo><mi>c</mi><mi>Δ</mi><mo>⋅</mo><mo>)</mo></math></span>, where Δ is the Euclidean Laplace operator and <em>c</em> is a positive constant. To prove the existence solution we introduced an appropriate structure of Hilbert spaces which allows us to use semigroups theory when the damping term is nonlinear. Using the Nehari manifold associated to the stationary problem, we create a stable set <span><math><mi>S</mi></math></span> such that, taking the initial data in <span><math><mi>S</mi></math></span>, the solution is global and the energy of the problem decay exponentially. In this case the damping is nonlinear and the source term satisfies the general assumption known as Ambrosetti-Rabinowitz condition. Moreover, under some appropriate conditions on the initial data we also prove a blow-up result with the source term subject to the Ambrosetti-Rabinowitz condition. Finally, we also prove a stability result with a more restrictive source term, which allows characterize the pass mountain level of the stationary problem.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"445 ","pages":"Article 113590"},"PeriodicalIF":2.4,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144490351","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":"Solutions with prescribed mass for the p-Laplacian Schrödinger-Poisson system with critical growth","authors":"Kai Liu , Xiaoming He , Vicenţiu D. Rădulescu","doi":"10.1016/j.jde.2025.113570","DOIUrl":"10.1016/j.jde.2025.113570","url":null,"abstract":"<div><div>In this paper, we focus on the existence and multiplicity of solutions for the <em>p</em>-Laplacian Schrödinger-Poisson system<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><mo>−</mo><msub><mrow><mi>Δ</mi></mrow><mrow><mi>p</mi></mrow></msub><mi>u</mi><mo>+</mo><mi>γ</mi><mi>ϕ</mi><msup><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>=</mo><mi>λ</mi><msup><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><mi>μ</mi><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><msup><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow><mrow><msup><mrow><mi>p</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>,</mo></mtd><mtd><mspace></mspace><mspace></mspace><mtext>in</mtext><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>ϕ</mi><mo>=</mo><msup><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow><mrow><mi>p</mi></mrow></msup><mo>,</mo></mtd><mtd><mspace></mspace><mspace></mspace><mtext>in</mtext><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo></mtd></mtr></mtable></mrow></math></span></span></span> with a prescribed mass given by<span><span><span><math><munder><mo>∫</mo><mrow><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></munder><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi></mrow></msup><mi>d</mi><mi>x</mi><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>,</mo></math></span></span></span> in the Sobolev critical case, where, <span><math><mn>1</mn><mo><</mo><mi>p</mi><mo><</mo><mn>3</mn><mo>,</mo><mi>a</mi><mo>></mo><mn>0</mn></math></span>, and <span><math><mi>γ</mi><mo>></mo><mn>0</mn></math></span>, <span><math><mi>μ</mi><mo>></mo><mn>0</mn></math></span> are parameters, <span><math><msup><mrow><mi>p</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>=</mo><mfrac><mrow><mn>3</mn><mi>p</mi></mrow><mrow><mn>3</mn><mo>−</mo><mi>p</mi></mrow></mfrac></math></span> is the Sobolev critical exponent, and <span><math><mi>λ</mi><mo>∈</mo><mi>R</mi></math></span> is an undetermined parameter, acting as a Lagrange multiplier. We investigate this system under the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-subcritical perturbation <span><math><mi>μ</mi><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi></math></span>, with <span><math><mi>q</mi><mo>∈</mo><mo>(</mo><mi>p</mi><mo>,</mo><mi>p</mi><mo>+</mo><mfrac><mrow><msup><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>3</mn></mrow></mfrac><mo>)</mo></math></span>, and establish the existence of multiple normalized solutions using the truncation technique, concentration-compactness ","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"444 ","pages":"Article 113570"},"PeriodicalIF":2.4,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144490447","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":"Heat-source type atmospheric nonlinear flow patterns in zonal cloud bands","authors":"C.I. Martin","doi":"10.1016/j.jde.2025.113589","DOIUrl":"10.1016/j.jde.2025.113589","url":null,"abstract":"<div><div>We present a family of exact solutions to a set of recently derived nonlinear equations governing at leading order the dynamics of flows in zonal cloud bands that resemble those on Jupiter. These solutions are radial in the horizontal variables, present density and temperature that decrease with height, a pressure function that decreases in the radial direction, and allow heat flowing out into the environment: these are features that are also observed in the Jupiter's Red Spot. Using a WKB analysis we show that certain exact solutions are stable under a specific choice of the density distribution.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"445 ","pages":"Article 113589"},"PeriodicalIF":2.4,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144490405","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":"Sharp lifespan estimates for semilinear fractional evolution equations with critical nonlinearity","authors":"Wenhui Chen , Giovanni Girardi","doi":"10.1016/j.jde.2025.113568","DOIUrl":"10.1016/j.jde.2025.113568","url":null,"abstract":"<div><div>In this paper we consider semilinear wave equation and semilinear second order <em>σ</em>-evolution equations with different (effective or non-effective) damping mechanisms driven by fractional Laplace operators; in particular, the nonlinear term is the product of a power nonlinearity <span><math><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi></mrow></msup></math></span> with the critical exponent <span><math><mi>p</mi><mo>=</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>)</mo></math></span> and a modulus of continuity <span><math><mi>μ</mi><mo>(</mo><mo>|</mo><mi>u</mi><mo>|</mo><mo>)</mo></math></span>. We derive a critical condition on the nonlinearity by proving a global in time existence result under the Dini condition on <em>μ</em> and a blow-up result when <em>μ</em> does not satisfy the Dini condition. Especially, in this latter case we determine new sharp estimates for the lifespan of local solutions, obtaining coincident upper and lower bounds of the lifespan. In particular, we derive a new sharp estimate for the wave equation with structural damping and classical power nonlinearity <span><math><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi></mrow></msup></math></span> in the critical case <span><math><mi>p</mi><mo>=</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>)</mo></math></span>, not yet determined in previous literature. The proof of the blow-up results and the upper bound estimates of the lifespan require the introduction of new test functions which allows to overcome some new difficulties due to the presence of both non-local differential operators and general nonlinearities.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"443 ","pages":"Article 113568"},"PeriodicalIF":2.4,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144491147","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}