Journal of Differential Equations最新文献

{"title":"From nonlinear Schrödinger equation to interacting particle system","authors":"Weiwei Ao,&nbsp;Juntao Lv,&nbsp;Kelei Wang","doi":"10.1016/j.jde.2025.113509","DOIUrl":"10.1016/j.jde.2025.113509","url":null,"abstract":"<div><div>We study the limiting behavior of solutions to nonlinear Schrödinger equations<span><span><span><math><mo>−</mo><msup><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>Δ</mi><msub><mrow><mi>u</mi></mrow><mrow><mi>ε</mi></mrow></msub><mo>+</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>ε</mi></mrow></msub><mo>=</mo><msubsup><mrow><mi>u</mi></mrow><mrow><mi>ε</mi></mrow><mrow><mi>p</mi></mrow></msubsup><mo>,</mo><mspace></mspace><msub><mrow><mi>u</mi></mrow><mrow><mi>ε</mi></mrow></msub><mo>&gt;</mo><mn>0</mn><mspace></mspace><mtext>in</mtext><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>,</mo></math></span></span></span> as <span><math><mi>ε</mi><mo>→</mo><mn>0</mn></math></span>, where <em>p</em> is Sobolev subcritical. These solutions are assumed to have infinitely many peaks. We derive the interaction form between the limiting peak points. This is achieved by first describing the main order term of <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>ε</mi></mrow></msub></math></span> and providing a very precise estimate on the error by the reverse Lyapunov-Schmidt reduction method, and then extracting information from the reduction equation in a limiting way.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"442 ","pages":"Article 113509"},"PeriodicalIF":2.4,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144230890","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":"Characterization of centers by their complex separatrices","authors":"Isaac A. García,&nbsp;Jaume Giné","doi":"10.1016/j.jde.2025.113506","DOIUrl":"10.1016/j.jde.2025.113506","url":null,"abstract":"<div><div>In this work, we address analytic families of real planar vector fields <span><math><msub><mrow><mi>X</mi></mrow><mrow><mi>λ</mi></mrow></msub></math></span> having a monodromic singularity at the origin for all parameters <span><math><mi>λ</mi><mo>∈</mo><mi>Λ</mi></math></span>, where Λ is an open subset of the real finite-dimensional Euclidean space. We assume that <span><math><msub><mrow><mi>X</mi></mrow><mrow><mi>λ</mi></mrow></msub></math></span> depends analytically on <em>λ</em>. This naturally leads to the so-called center-focus problem, which consists of describing the partition of Λ induced by the centers and the foci at the origin. We provide a characterization of the centers (whether degenerate or not) in terms of a specific integral of the cofactor associated with a real invariant analytic curve passing through the singularity, which always exists. Several consequences and applications are also discussed.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"442 ","pages":"Article 113506"},"PeriodicalIF":2.4,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144230891","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":"Characterization results for a third-order evolution equation with memory and infinite history","authors":"Eduardo H. Gomes Tavares ,&nbsp;Mauricio Barbosa da Silva ,&nbsp;Jinyun Yuan","doi":"10.1016/j.jde.2025.113494","DOIUrl":"10.1016/j.jde.2025.113494","url":null,"abstract":"<div><div>The characterization of certain properties related to a third-order evolution equation with memory and infinite history will be discussed in this work. It is well-known that the existence and stability of solutions for equations of this nature depend on a relation between their parameters. By exploring classical tools from the semigroup theory of linear operators and working with a more general class of memory kernels, it will be proven here that such a relation is a sufficient and necessary condition for these properties.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"442 ","pages":"Article 113494"},"PeriodicalIF":2.4,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144230896","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":"Emergent dynamics of the Kuramoto model with adaptive coupling on undirected networks","authors":"Yu-Qing Wang,&nbsp;Jiu-Gang Dong","doi":"10.1016/j.jde.2025.113475","DOIUrl":"10.1016/j.jde.2025.113475","url":null,"abstract":"<div><div>We study the emergent dynamics for the Kuramoto model with adaptive and local couplings. With conditions satisfied by network topology, sufficient frameworks for the complete synchronization and phase-locking estimates are established in terms of initial configurations and system parameters. For a homogeneous ensemble with Hebbian adaptive coupling, we demonstrate that complete phase synchronization occurs exponentially on connected symmetric networks for initial phase confined in a quarter circle. When initial phase diameters exceed <span><math><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></math></span>, synchronization is achieved under stricter scrambling undirected networks and admissible coupling strength. Moreover, complete frequency synchronization is guaranteed unconditionally. For a homogeneous ensemble with anti-Hebbian adaptive coupling, we prove that the complete phase synchronization emerges on connected symmetric network when initial configurations are located on the same semicircle. For a heterogeneous ensemble with Hebbian adaptive coupling, we establish the emergence of phase-locked state under two frameworks: scrambling undirected networks with initial phase diameter below <span><math><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></math></span> and admissible coupling strength, and connected undirected networks with restricted initial phase configuration. Both ensure complete frequency synchronization and convergence to an equilibrium. Moreover, a practical phase synchronization is proved on connected symmetric network with anti-Hebbian adaptive coupling when initial configurations are located on the same semicircle. Finally, numerical simulations are provided to demonstrate our theoretical results.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"441 ","pages":"Article 113475"},"PeriodicalIF":2.4,"publicationDate":"2025-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144222882","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":"Regularity for fully nonlinear elliptic equations with natural growth in gradient and singular nonlinearity","authors":"Mohan Mallick ,&nbsp;Ram Baran Verma","doi":"10.1016/j.jde.2025.113477","DOIUrl":"10.1016/j.jde.2025.113477","url":null,"abstract":"<div><div>In this article, we consider the following boundary value problem:<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><mi>F</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>D</mi><mi>u</mi><mo>,</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>)</mo><mo>+</mo><mi>c</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>u</mi><mo>+</mo><mi>p</mi><mo>(</mo><mi>x</mi><mo>)</mo><msup><mrow><mi>u</mi></mrow><mrow><mo>−</mo><mi>α</mi></mrow></msup></mtd><mtd><mo>=</mo><mn>0</mn><mspace></mspace><mtext>in</mtext><mspace></mspace><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><mi>u</mi></mtd><mtd><mo>=</mo><mn>0</mn><mspace></mspace><mtext>on</mtext><mspace></mspace><mo>∂</mo><mi>Ω</mi><mo>,</mo></mtd></mtr></mtable></mrow></math></span></span></span> where Ω is a bounded and <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> smooth domain in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>. The operator <em>F</em> is proper and has superlinear growth in gradient. This study examines the boundary behavior of the solutions to the above equation and establishes a global regularity result similar to that established in <span><span>[11]</span></span>, <span><span>[15]</span></span>, which involves linear growth in the gradient.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"441 ","pages":"Article 113477"},"PeriodicalIF":2.4,"publicationDate":"2025-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144222883","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":"The small diffusion limit of the principal eigenvalue problems with advection","authors":"Yujin Guo ,&nbsp;Yuan Lou ,&nbsp;Hongfei Zhang","doi":"10.1016/j.jde.2025.113473","DOIUrl":"10.1016/j.jde.2025.113473","url":null,"abstract":"<div><div>This paper is concerned with the following second order principal eigenvalue problem with an advection term:<span><span><span><math><mo>−</mo><mi>ε</mi><mi>Δ</mi><mi>ϕ</mi><mo>−</mo><mn>2</mn><mi>α</mi><mi>∇</mi><mi>m</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>⋅</mo><mi>∇</mi><mi>ϕ</mi><mo>+</mo><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>ϕ</mi><mo>=</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>ε</mi></mrow></msub><mi>ϕ</mi><mspace></mspace><mspace></mspace><mspace></mspace><mtext>in</mtext><mspace></mspace><mspace></mspace><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></math></span></span></span> where <span><math><mi>Ω</mi><mo>⊆</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mspace></mspace><mo>(</mo><mi>N</mi><mo>≥</mo><mn>1</mn><mo>)</mo></math></span> is a bounded domain with smooth boundary ∂Ω and contains the origin as an interior point, the constants <span><math><mi>ε</mi><mo>&gt;</mo><mn>0</mn></math></span> and <span><math><mi>α</mi><mo>&gt;</mo><mn>0</mn></math></span> are the diffusive and advection coefficients, respectively, and <span><math><mi>m</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mover><mrow><mi>Ω</mi></mrow><mrow><mo>¯</mo></mrow></mover><mo>)</mo></math></span>, <span><math><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mi>γ</mi></mrow></msup><mo>(</mo><mover><mrow><mi>Ω</mi></mrow><mrow><mo>¯</mo></mrow></mover><mo>)</mo><mspace></mspace><mo>(</mo><mn>0</mn><mo>&lt;</mo><mi>γ</mi><mo>&lt;</mo><mn>1</mn><mo>)</mo></math></span> are given functions. We investigate the refined limiting profiles of the principal eigenpair for the above eigenvalue problem in the small diffusion limit (<em>i.e.</em>, <span><math><mi>ε</mi><mo>→</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msup></math></span>), where the advection term <span><math><mi>m</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> can be degenerate.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"441 ","pages":"Article 113473"},"PeriodicalIF":2.4,"publicationDate":"2025-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144222951","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":"Convergence rates toward the planar stationary solution for a hyperbolic-elliptic coupled system with boundary effect corresponding to shock wave","authors":"Shanming Ji,&nbsp;Minyi Zhang,&nbsp;Changjiang Zhu","doi":"10.1016/j.jde.2025.113492","DOIUrl":"10.1016/j.jde.2025.113492","url":null,"abstract":"<div><div>In this paper, we study the asymptotic behavior of solutions to an initial-boundary value problem for a hyperbolic-elliptic coupled system of the radiating gas on half space with the conditions <span><math><mi>u</mi><mo>(</mo><mn>0</mn><mo>,</mo><mi>y</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>=</mo><msub><mrow><mi>u</mi></mrow><mrow><mo>−</mo></mrow></msub></math></span> and <span><math><mi>u</mi><mo>(</mo><mo>∞</mo><mo>,</mo><mi>y</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>=</mo><msub><mrow><mi>u</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>&lt;</mo><msub><mrow><mi>u</mi></mrow><mrow><mo>−</mo></mrow></msub></math></span>, where the corresponding Cauchy problem admits the shock wave as an asymptotic profile. In the case of <span><math><msub><mrow><mi>u</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>&lt;</mo><msub><mrow><mi>u</mi></mrow><mrow><mo>−</mo></mrow></msub><mo>≤</mo><mn>0</mn></math></span>, we prove that the solution to the problem converges to the corresponding planar stationary solution as time tends to infinity by assuming that the initial perturbation is small. Furthermore, we obtain the convergence rate by applying the time and space weighted energy method. The results include one-dimensional and two-dimensional cases.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"442 ","pages":"Article 113492"},"PeriodicalIF":2.4,"publicationDate":"2025-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144230897","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":"Convergence to SPDEs for second order evolutionary equation with singular short–range correlated potential","authors":"Dong Su ,&nbsp;Wei Wang","doi":"10.1016/j.jde.2025.113497","DOIUrl":"10.1016/j.jde.2025.113497","url":null,"abstract":"<div><div>The random homogenization for second order evolutionary equation with singular short–range correlated potential is derived. Comparing with the first order evolutionary equation, more difficulty need to be overcome in the moment estimation of the solution due to non–symmetrical semigroup of second order evolutionary equation. In our approach the solution is written out by the Duhamel's formula and the moment estimation of the solution is obtained by some analytic methods. Then by means of diagrammatic expansions and chaos expansions, the solution is shown to converge in distribution to the solution of stochastic partial differential equations (SPDEs) in Stratonovich form driven by spatial white noise.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"442 ","pages":"Article 113497"},"PeriodicalIF":2.4,"publicationDate":"2025-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144230904","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":"Optimal decay rates for the compressible Navier–Stokes equations with density–dependent viscosities","authors":"Zhen Luo,&nbsp;Wanying Yang","doi":"10.1016/j.jde.2025.113483","DOIUrl":"10.1016/j.jde.2025.113483","url":null,"abstract":"<div><div>This paper concerns the Cauchy problem for the compressible Navier–Stokes equations with density-dependent viscosities, and the optimal decay rates of all higher order spatial derivatives of the solutions are obtained. We also prove the same optimal decay rates of solution to the shallow water equations with capillarity. The proof relies on applying the high-low frequency decomposition in the pure energy estimates developed by Guo and Wang (2012) <span><span>[11]</span></span>, both linearly and nonlinearly.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"441 ","pages":"Article 113483"},"PeriodicalIF":2.4,"publicationDate":"2025-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144222881","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":"Global quasi-neutral limit for a two-fluid non-isentropic Euler-Poisson system in several space dimensions","authors":"Wan-Di Lu,&nbsp;Yong-Fu Yang","doi":"10.1016/j.jde.2025.113485","DOIUrl":"10.1016/j.jde.2025.113485","url":null,"abstract":"<div><div>The aim of this paper is to investigate the global quasi-neutral limit to the Cauchy problem for a two-fluid non-isentropic Euler-Poisson system in several space dimensions. We prove that the system converges globally to the non-isentropic Euler equations as the Debye length tends to zero. This problem is studied for smooth solutions near the constant equilibrium state. To establish these results, uniform energy estimates and various dissipation estimates are derived. Furthermore, the global convergence rate is obtained as well.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"441 ","pages":"Article 113485"},"PeriodicalIF":2.4,"publicationDate":"2025-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144222333","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}