Journal of Differential Equations最新文献

{"title":"Multiple normalized solutions for Schrödinger-Maxwell equation with Sobolev critical exponent and mixed nonlinearities","authors":"Jin-Cai Kang , Yong-Yong Li , Chun-Lei Tang","doi":"10.1016/j.jde.2025.113564","DOIUrl":"10.1016/j.jde.2025.113564","url":null,"abstract":"<div><div>In this paper, we study the Schrödinger-Maxwell equation with critical growth<span><span><span><math><mrow><mrow><mo>{</mo><mtable><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>λ</mi><mi>u</mi><mo>+</mo><mi>κ</mi><mrow><mo>(</mo><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>⁎</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mi>u</mi><mo>=</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>4</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><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><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><mn>2</mn></mrow></msup><mi>d</mi><mi>x</mi><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo></mtd></mtr></mtable></mrow></mrow></math></span></span></span> where <span><math><mi>a</mi><mo>></mo><mn>0</mn></math></span> is prescribed, <span><math><mi>κ</mi><mo>></mo><mn>0</mn></math></span>, <span><math><mi>μ</mi><mo>∈</mo><mi>R</mi></math></span>, <span><math><mn>2</mn><mo><</mo><mi>q</mi><mo><</mo><mn>6</mn></math></span>, ⁎ denotes the convolution and <span><math><mi>λ</mi><mo>∈</mo><mi>R</mi></math></span> appears as a Lagrange multiplier. Motivated by the works of Wei and Wu (2022) <span><span>[41]</span></span> for <span><math><mi>κ</mi><mo>=</mo><mn>0</mn></math></span> and Bellazzini and Siciliano (2011) <span><span>[5]</span></span> for homogeneous nonlinearity, we get two normalized solutions when <span><math><mi>q</mi><mo>∈</mo><mo>(</mo><mn>2</mn><mo>,</mo><mfrac><mrow><mn>8</mn></mrow><mrow><mn>3</mn></mrow></mfrac><mo>)</mo></math></span> and <span><math><mi>μ</mi><mo>></mo><mn>0</mn></math></span>, one of which is ground state normalized solution. It is worth emphasizing that the method of Schwarz spherical rearrangement is invalid for the case of <span><math><mi>κ</mi><mo>></mo><mn>0</mn></math></span>, different from the case of <span><math><mi>κ</mi><mo>=</mo><mn>0</mn></math></span>, and it is hard to establish the strictly subadditive inequality of least energy to exclude the dichotomy of minimizing sequence standardly. To our knowledge, the existence of second solution for the above problem has not been addressed in the current literatures. Moreover, we will show a nonexistence result of positive normalized solution when <span><math><mi>μ</mi><mo>≤</mo><mn>0</mn></math></span> and <span><math><mi>q</mi><mo>∈</mo><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></span>, which can be regarded as a generalization and improvement of Jeanjean and Le (2021) <span><span>[21]</span></span> from the case of <span><math><mi","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"443 ","pages":"Article 113564"},"PeriodicalIF":2.4,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144321678","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 upper semi-continuity of random attractors to the stochastic evolution equations driven by rough path with Hurst index H∈(13,12]","authors":"Qiyong Cao,&nbsp;Hongjun Gao","doi":"10.1016/j.jde.2025.113552","DOIUrl":"10.1016/j.jde.2025.113552","url":null,"abstract":"<div><div>In this paper, we consider the upper semi-continuity of the random attractors for a class of evolution equations driven by smooth stationary fractional noise with Hurst index <span><math><mi>H</mi><mo>∈</mo><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac><mo>,</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>]</mo></math></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"444 ","pages":"Article 113552"},"PeriodicalIF":2.4,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144313629","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 stability of sharp fronts: Analysis and rigorous computation","authors":"Blake Barker ,&nbsp;Jared C. Bronski ,&nbsp;Vera Mikyoung Hur ,&nbsp;Zhao Yang","doi":"10.1016/j.jde.2025.113550","DOIUrl":"10.1016/j.jde.2025.113550","url":null,"abstract":"<div><div>We investigate the stability of traveling front solutions to nonlinear diffusive-dispersive equations of Burgers type, with a primary focus on the Korteweg-de Vries–Burgers (KdVB) equation, although our analytical findings extend more broadly. Manipulating the temporal modulation of the translation parameter of the front and employing the energy method, we establish asymptotic, nonlinear, and orbital stability, provided that an auxiliary Schrödinger equation possesses precisely one bound state. Notably, our result is independent of the monotonicity of the profile and does not necessitate the initial condition to be close to the front. We identify a sufficient condition for stability based on a functional that characterizes the ‘width’ of the traveling wave profile. Analytical verification for the KdVB equation confirms that this sufficient condition holds for the relative dispersion parameter within an open interval <span><math><mo>⊃</mo><mo>[</mo><mo>−</mo><mn>0.25</mn><mo>,</mo><mn>0.25</mn><mo>]</mo></math></span>, encompassing all monotone profiles. Utilizing validated numerics or rigorous computation, we present a computer-assisted proof demonstrating that the stability condition itself holds for parameter values within the interval <span><math><mo>[</mo><mn>0.2533</mn><mo>,</mo><mn>3.9</mn><mo>]</mo></math></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"444 ","pages":"Article 113550"},"PeriodicalIF":2.4,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144312767","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":"Symmetry breaking bifurcation and the stability of stationary solutions of a phase-field model","authors":"Yasuhito Miyamoto ,&nbsp;Tatsuki Mori ,&nbsp;Sohei Tasaki ,&nbsp;Tohru Tsujikawa ,&nbsp;Shoji Yotsutani","doi":"10.1016/j.jde.2025.113500","DOIUrl":"10.1016/j.jde.2025.113500","url":null,"abstract":"<div><div>We have been investigating the global bifurcation diagrams of stationary solutions for a phase field model proposed by Fix and Caginalp in a one-dimensional case. It has recently been shown that there exists a secondary bifurcation with a symmetry-breaking phenomenon from a branch consisting of symmetric solutions in the case where the total enthalpy equals zero. In this paper, we determine the stability/instability of all symmetric solutions and asymmetric solutions near the secondary bifurcation point. Moreover, we show representation formulas for all eigenvalues and eigenfunctions for the linearized eigenvalue problem around the symmetric solutions.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"441 ","pages":"Article 113500"},"PeriodicalIF":2.4,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144306837","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 existence and optimal decay rates of strong solutions to the equilibrium diffusion model arising in radiation hydrodynamics","authors":"Peng Jiang ,&nbsp;Fucai Li ,&nbsp;Jinkai Ni","doi":"10.1016/j.jde.2025.113557","DOIUrl":"10.1016/j.jde.2025.113557","url":null,"abstract":"<div><div>In this paper, we investigate the global existence and optimal decay rates of strong solutions in the critical Sobolev space <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math></span> to the equilibrium diffusion model arising in radiation hydrodynamics. This model is composed of the full compressible Navier-Stokes equations with radiation diffusion terms. Assuming that the initial data <span><math><mo>(</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></math></span> is sufficiently small in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm, we establish the global existence of strong solutions near the equilibrium state <span><math><mo>(</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> by applying the refined energy method. Then, by performing Fourier analysis techniques and exploiting the frequency decomposition method, we get the optimal time-decay rates of strong solutions (including the highest order spatial derivatives) in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm. In particular, the lower bound of time-decay rates of strong solutions is also obtained by making use of Hodge decomposition, delicate spectral analysis and the theory of Besov space. In addition, we obtain the exponential decay of strong solutions in the periodic domain case.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"443 ","pages":"Article 113557"},"PeriodicalIF":2.4,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144307522","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 Gierer-Meinhardt system in the entire space with non-local proliferation rates","authors":"Marius Ghergu ,&nbsp;Nikos I. Kavallaris ,&nbsp;Yasuhito Miyamoto","doi":"10.1016/j.jde.2025.113559","DOIUrl":"10.1016/j.jde.2025.113559","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In this work, we present a novel stationary Gierer-Meinhardt system incorporating non-local proliferation rates, defined as follows:&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;mo&gt;−&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;ρ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mtext&gt; in &lt;/mtext&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mtext&gt; in &lt;/mtext&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&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; This system emerges in various contexts, such as biological morphogenesis, where two interacting chemicals, identified as an activator and an inhibitor, are described, and in ecological systems modeling the interaction between two species, classified as specialists and generalists. The non-local interspecies interactions are represented by the terms &lt;span&gt;&lt;math&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; where the ⁎-symbol denotes the convolution operation in &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; with a kernel &lt;span&gt;&lt;math&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&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;/math&gt;&lt;/span&gt;. In the system, we assume that &lt;span&gt;&lt;math&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;ρ&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;mi&gt;γ&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;, while the parameters satisfy &lt;span&gt;&lt;math&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;. Under various integrability conditions on the kernel &lt;em&gt;J&lt;/em&gt;, we establish the existence and non-existence of classical positive solutions in the function space &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"444 ","pages":"Article 113559"},"PeriodicalIF":2.4,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144308080","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":"Long-time behaviors of some stochastic differential equations driven by Lévy noise","authors":"I. Orlovskyi ,&nbsp;F. Proske ,&nbsp;O. Tymoshenko","doi":"10.1016/j.jde.2025.113561","DOIUrl":"10.1016/j.jde.2025.113561","url":null,"abstract":"<div><div>Using key tools such as Itô's formula for general semi-martingales, moment estimates for Lévy-type stochastic integrals, and properties of regularly varying functions we find conditions under which solutions of a stochastic differential equation with jumps are almost surely asymptotically equivalent to a nonrandom function as <span><math><mi>t</mi><mo>→</mo><mo>∞</mo></math></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"442 ","pages":"Article 113561"},"PeriodicalIF":2.4,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144290710","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":"Uniqueness of weak solutions to the primitive equations in some anisotropic spaces","authors":"Tim Binz ,&nbsp;Yoshiki Iida","doi":"10.1016/j.jde.2025.113554","DOIUrl":"10.1016/j.jde.2025.113554","url":null,"abstract":"<div><div>We consider the both 3D and 2D viscous primitive equations for ocean in the isothermal setting. While strong global well-posedness of the viscous primitive equations for large data in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> has already proved, the uniqueness of the weak solutions of Leray–Hope type for given initial data in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> remains an outstanding open problem. In this paper, we establish a new conditional uniqueness result for weak solutions to the primitive equations, that is, if a weak solution belongs some scaling invariant function spaces, and satisfies some additional assumptions, then the weak solution is unique. In particular, our result can be obtained as different one from <em>z</em>-weak solutions framework by adopting some anisotropic approaches with the homogeneous toroidal Besov spaces. As an application of the proof, we establish the energy equality for weak solutions in the uniqueness class given in the main theorem.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"444 ","pages":"Article 113554"},"PeriodicalIF":2.4,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144290763","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":"Propagation dynamics of a nonautonomous epidemic system with nonlocal diffusion","authors":"Xiongxiong Bao ,&nbsp;Zhucheng Jin","doi":"10.1016/j.jde.2025.113562","DOIUrl":"10.1016/j.jde.2025.113562","url":null,"abstract":"<div><div>This paper investigates the spreading speeds and generalized traveling wave solutions for a time-dependent epidemic system with nonlocal dispersal. In this nonautonomous epidemic system, both the nonlocal dispersal kernel and the coefficients in reaction terms are general time heterogeneous and possess uniform mean values. To characterize the spreading speed of the system, we first establish the spreading speed of a scalar nonautonomous KPP equation. Then, using a derived key pointwise estimate, we compare the solution of the system with that of the scalar KPP equation and thus obtain the spreading speed of the system. Combining with the spreading speed results, we demonstrate the nonexistence of generalized traveling wave solutions with small wave speeds in average sense. By constructing proper super and sub solutions, we establish the existence of generalized traveling wave solutions and explore the limiting behavior of the wave profile using the uniform persistence theory.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"444 ","pages":"Article 113562"},"PeriodicalIF":2.4,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144290762","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":"Lipschitz estimates in the Besov settings for Young and rough differential equations","authors":"Peter K. Friz ,&nbsp;Hannes Kern ,&nbsp;Pavel Zorin-Kranich","doi":"10.1016/j.jde.2025.113507","DOIUrl":"10.1016/j.jde.2025.113507","url":null,"abstract":"<div><div>We develop a set of techniques that enable us to effectively recover Besov rough analysis from <em>p</em>-variation rough analysis. Central to our approach are new metric groups, in which some objects in rough path theory that have been previously viewed as two-parameter can be considered as path increments. Furthermore, we develop highly precise Lipschitz estimates for Young and rough differential equations, both in the variation and Besov scale.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"443 ","pages":"Article 113507"},"PeriodicalIF":2.4,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144291143","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}