Journal of Differential Equations最新文献

{"title":"Well-posedness of stochastic chemotaxis system","authors":"Yunfeng Chen ,&nbsp;Jianliang Zhai ,&nbsp;Tusheng Zhang","doi":"10.1016/j.jde.2025.113531","DOIUrl":"10.1016/j.jde.2025.113531","url":null,"abstract":"<div><div>In this paper, we establish the existence and uniqueness of solutions of elliptic-parabolic stochastic Keller-Segel systems. The solution is obtained through a carefully designed localization procedure together with some a priori estimates. Both noise of linear growth and nonlinear noise are considered. The <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> Itô formula plays an important role.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"442 ","pages":"Article 113531"},"PeriodicalIF":2.4,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144254904","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":"On a coupled-physics transmission eigenvalue problem and its spectral properties with applications","authors":"Huaian Diao ,&nbsp;Hongyu Liu ,&nbsp;Qingle Meng ,&nbsp;Li Wang","doi":"10.1016/j.jde.2025.113508","DOIUrl":"10.1016/j.jde.2025.113508","url":null,"abstract":"<div><div>In this paper, we investigate a transmission eigenvalue problem that couples the principles of acoustics and elasticity. This problem naturally arises when studying fluid-solid interactions and constructing bubbly-elastic structures to create metamaterials. We uncover intriguing local geometric structures of the transmission eigenfunctions near the corners of the domains, under typical regularity conditions. As applications, we present novel unique identifiability and visibility results for an inverse problem associated with an acoustoelastic system, which hold practical significance.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"441 ","pages":"Article 113508"},"PeriodicalIF":2.4,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144254785","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":"On well/ill-posedness for the generalized surface quasi-geostrophic equation in Hölder spaces","authors":"Young-Pil Choi ,&nbsp;Jinwook Jung ,&nbsp;Junha Kim","doi":"10.1016/j.jde.2025.113521","DOIUrl":"10.1016/j.jde.2025.113521","url":null,"abstract":"<div><div>We establish the well/ill-posedness theories for the inviscid <em>α</em>-surface quasi-geostrophic (<em>α</em>-SQG) equation in Hölder spaces, where <span><math><mi>α</mi><mo>=</mo><mn>0</mn></math></span> and <span><math><mi>α</mi><mo>=</mo><mn>1</mn></math></span> correspond to the two-dimensional Euler equation in the vorticity formulation and SQG equation of geophysical significance, respectively. We first prove the local-in-time well-posedness of <em>α</em>-SQG equation in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo><mo>;</mo><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn><mo>,</mo><mi>β</mi></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>)</mo></math></span> with <span><math><mi>β</mi><mo>∈</mo><mo>(</mo><mi>α</mi><mo>,</mo><mn>1</mn><mo>)</mo></math></span> for some <span><math><mi>T</mi><mo>&gt;</mo><mn>0</mn></math></span>. We then analyze the strong ill-posedness in <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn><mo>,</mo><mi>α</mi></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> constructing smooth solutions to the <em>α</em>-SQG equation that exhibit <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn><mo>,</mo><mi>α</mi></mrow></msup></math></span>–norm growth in a short time. In particular, we develop the nonexistence theory for <em>α</em>-SQG equation in <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn><mo>,</mo><mi>α</mi></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"443 ","pages":"Article 113521"},"PeriodicalIF":2.4,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144263883","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":"Spectrum for a weighted one-dimensional fractional Laplace operator","authors":"Bianxia Yang ,&nbsp;Zhijiang Zhang ,&nbsp;Ruyun Ma","doi":"10.1016/j.jde.2025.113501","DOIUrl":"10.1016/j.jde.2025.113501","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In this paper, we study the spectrum of the one-dimensional fractional Laplace operator with a definite weight&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mtext&gt;in&lt;/mtext&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mo&gt;∖&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; is the one-dimensional fractional Laplace nonlocal operator. By virtue of Γ-convergence arguments, we investigate, in the singular limit, that the eigenvalue and eigenfunction of the nonlocal operator converge to those of the corresponding classical second-order two-point boundary value problem in the first place, and then, building upon the continuity of the eigenvalues and eigenfunctions as a function of fractional index, we derive the simplicity of the eigenvalues of the fractional Laplace nonlocal operator for all fractional index &lt;span&gt;&lt;math&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; by adopting a stet-by-step iterative approach. Furthermore, using the &lt;em&gt;α&lt;/em&gt;-harmonic extension, we receive that the corresponding eigenfunction &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;φ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; has at most &lt;span&gt;&lt;math&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; zeros in &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. At last, from an experiment point of view, we give the numerical eigenvalues and eigenfunctions of the weighted fractional Laplace problem by means of the finite element method in some special cases, which enriches","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"443 ","pages":"Article 113501"},"PeriodicalIF":2.4,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144253679","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":"Population dynamics in closed polluted aquatic ecosystems with time-periodic input of toxicants","authors":"Zhenzhen Li,&nbsp;Zhi-An Wang","doi":"10.1016/j.jde.2025.113502","DOIUrl":"10.1016/j.jde.2025.113502","url":null,"abstract":"<div><div>This paper is concerned with a diffusive population-toxicant system in a polluted aquatic environment with temporally periodic and spatially heterogeneous input of toxicants. By a variety of mathematical tools, such as the principal eigenvalue theory, method of upper-lower solutions, theory of monotone semi-flow, implicit function theorem, etc., we derive sufficient conditions on the existence and global stability of periodic solutions with fixed diffusion rates and explore the asymptotic profiles of positive periodic solutions for large and small diffusion rates. Our results show that if the toxicity of toxicants is low (resp. high), then the aquatic population persists (resp. becomes extinct), while both persistence and extinction may be locally stable (i.e. bi-stability) for moderate toxicity of toxicants. We also find that the spatial distribution of positive periodic solutions with small diffusion rates is quite different from that with large diffusion rates.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"442 ","pages":"Article 113502"},"PeriodicalIF":2.4,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144254905","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":"Topological classification of global dynamics of planar polynomial Hamiltonian systems with separable variables","authors":"Xuemeng Sun,&nbsp;Dongmei Xiao","doi":"10.1016/j.jde.2025.113496","DOIUrl":"10.1016/j.jde.2025.113496","url":null,"abstract":"<div><div>In the paper, we completely characterize the local dynamics of polynomial Hamiltonian systems with separable variables and provide a method to determine its global dynamics on Poincaré disk. It is shown that there are three (four) topological classifications for finite (infinite, resp.) singular points of the Hamiltonian system with any degree <em>n</em>, and its global dynamics can be determined by the number of singular points and their separatrix skeleton. This provides an approach to characterize the topological classification of real algebraic curves <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>+</mo><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>y</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></span> in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, where <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></span> and <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>y</mi><mo>)</mo></math></span> are real polynomials of degrees <em>m</em> and <em>n</em>, respectively.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"443 ","pages":"Article 113496"},"PeriodicalIF":2.4,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144241196","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 boundedness and blow-up in a repulsive chemotaxis-consumption system in higher dimensions","authors":"Jaewook Ahn ,&nbsp;Kyungkeun Kang ,&nbsp;Dongkwang Kim","doi":"10.1016/j.jde.2025.113503","DOIUrl":"10.1016/j.jde.2025.113503","url":null,"abstract":"<div><div>This paper investigates the repulsive chemotaxis-consumption model<span><span><span><math><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>=</mo><mi>∇</mi><mo>⋅</mo><mo>(</mo><mi>D</mi><mo>(</mo><mi>u</mi><mo>)</mo><mi>∇</mi><mi>u</mi><mo>)</mo><mo>+</mo><mi>∇</mi><mo>⋅</mo><mo>(</mo><mi>u</mi><mi>∇</mi><mi>v</mi><mo>)</mo><mo>,</mo><mn>0</mn><mo>=</mo><mi>Δ</mi><mi>v</mi><mo>−</mo><mi>u</mi><mi>v</mi><mo>,</mo></math></span></span></span> in an <em>n</em>-dimensional ball, <span><math><mi>n</mi><mo>≥</mo><mn>3</mn></math></span>, where the diffusion coefficient <em>D</em> is an appropriate extension of the function <span><math><mn>0</mn><mo>≤</mo><mi>ξ</mi><mo>↦</mo><msup><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>ξ</mi><mo>)</mo></mrow><mrow><mi>m</mi><mo>−</mo><mn>1</mn></mrow></msup></math></span> for <span><math><mi>m</mi><mo>&gt;</mo><mn>0</mn></math></span>. Under the boundary conditions<span><span><span><math><mi>ν</mi><mo>⋅</mo><mo>(</mo><mi>D</mi><mo>(</mo><mi>u</mi><mo>)</mo><mi>∇</mi><mi>u</mi><mo>+</mo><mi>u</mi><mi>∇</mi><mi>v</mi><mo>)</mo><mo>=</mo><mn>0</mn><mspace></mspace><mtext> and </mtext><mspace></mspace><mi>v</mi><mo>=</mo><mi>M</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo></math></span></span></span> we demonstrate that for <span><math><mi>m</mi><mo>&gt;</mo><mn>1</mn></math></span>, or <span><math><mi>m</mi><mo>=</mo><mn>1</mn></math></span> and <span><math><mn>0</mn><mo>&lt;</mo><mi>M</mi><mo>&lt;</mo><mn>2</mn><mo>/</mo><mo>(</mo><mi>n</mi><mo>−</mo><mn>2</mn><mo>)</mo></math></span>, the system admits globally bounded classical solutions for any choice of sufficiently smooth radial initial data. This result is further extended to the case <span><math><mn>0</mn><mo>&lt;</mo><mi>m</mi><mo>&lt;</mo><mn>1</mn></math></span> when <em>M</em> is chosen to be sufficiently small, depending on the initial conditions. In contrast, it is shown that for <span><math><mn>0</mn><mo>&lt;</mo><mi>m</mi><mo>&lt;</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></mfrac></math></span>, the system exhibits blow-up behavior for sufficiently large <em>M</em>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"443 ","pages":"Article 113503"},"PeriodicalIF":2.4,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144241197","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":"Decay rates for star-shaped degenerate heat-wave coupled networks","authors":"Jia-Xian Guang,&nbsp;Zhong-Jie Han","doi":"10.1016/j.jde.2025.113505","DOIUrl":"10.1016/j.jde.2025.113505","url":null,"abstract":"<div><div>This work investigates the long-time dynamics of a star-shaped network composed of degenerate heat and wave equations. The well-posedness of the system is proved by standard semigroup theories and a comprehensive criterion for strong stability in such degenerate partial differential equations (PDE) networks is established. Through frequency domain analysis, the polynomial decay rate is explored in two scenarios: networks with a single wave equation, where the explicit decay rate depends solely on the degree of degeneration in those diffusion coefficients of the heat parts, and networks with multiple wave equations, where the explicit decay rates are derived under specific irrationality conditions on the spatial lengths of the wave equations involved in the network using Diophantine approximation arguments. Finally, a generalized slow decay rate is derived, providing a broader understanding of the long-time behavior of this complex degenerate heat-wave networks.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"443 ","pages":"Article 113505"},"PeriodicalIF":2.4,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144241195","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 degenerate linear kinetic equations with non-isothermal boundary conditions","authors":"Armand Bernou","doi":"10.1016/j.jde.2025.113470","DOIUrl":"10.1016/j.jde.2025.113470","url":null,"abstract":"<div><div>We study the degenerate linear Boltzmann equation inside a bounded domain with a generalized diffuse reflection at the boundary and variable temperature, including the Maxwell boundary conditions with the wall Maxwellian or heavy-tailed reflection kernel and the Cercignani-Lampis boundary condition. Our abstract collisional setting applies to the linear BGK model, the relaxation towards a space-dependent steady state, and collision kernels with fat tails. We prove for the first time the existence of a steady state and a rate of convergence towards it without assumptions on the temperature variations. Our results for the Cercignani-Lampis boundary condition make also no hypotheses on the accommodation coefficients. The proven rate is exponential when a control condition on the degeneracy of the collision operator is satisfied, and only polynomial when this assumption is not met, in line with our previous results regarding the free-transport equation. We also provide a precise description of the different convergence rates, including lower bounds, when the steady state is bounded. Our method yields constructive constants.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"442 ","pages":"Article 113470"},"PeriodicalIF":2.4,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144239538","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":"On the structure of the geometric tangent cone to the Wasserstein space","authors":"Averil Aussedat","doi":"10.1016/j.jde.2025.113520","DOIUrl":"10.1016/j.jde.2025.113520","url":null,"abstract":"<div><div>This article focuses on the metric orthogonal of the geometric tangent cone to the Wasserstein space. Some algebraic and topological properties are given, as well as a complete characterization and weak closedness property in dimension 1. It is shown that in general, the directional derivative of the Wasserstein distance is not sufficient to differentiate between the tangent cone and its orthogonal. To conclude, a general Helmholtz-Hodge decomposition is proved for measure fields.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"442 ","pages":"Article 113520"},"PeriodicalIF":2.4,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144239795","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}