Journal of Differential Equations最新文献

{"title":"Positive periodic solutions to the planar Lp dual Minkowski problem in the critical case","authors":"Zhibo Cheng ,&nbsp;Shujing Yuan ,&nbsp;Qigang Yuan ,&nbsp;Jingli Ren","doi":"10.1016/j.jde.2025.113776","DOIUrl":"10.1016/j.jde.2025.113776","url":null,"abstract":"<div><div>In this paper, we investigate the planar <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> dual Minkowski problem<span><span><span><math><msup><mrow><mi>x</mi></mrow><mrow><mo>″</mo></mrow></msup><mo>+</mo><mi>x</mi><mo>=</mo><msup><mrow><mi>x</mi></mrow><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow></msup><msup><mrow><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>x</mi></mrow><mrow><mo>′</mo><mspace></mspace><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mfrac><mrow><mn>2</mn><mo>−</mo><mi>q</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>,</mo></math></span></span></span> where <em>p</em> and <em>q</em> are two constants, <span><math><mi>f</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mi>R</mi><mo>/</mo><mi>T</mi><mi>Z</mi><mo>;</mo><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>)</mo></math></span>, and <span><math><mi>T</mi><mo>&gt;</mo><mn>0</mn></math></span>. Notice that in the critical case <span><math><mi>T</mi><mo>=</mo><mi>π</mi></math></span>, the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> dual Minkowski problem is closely related to the half-period symmetry problem in convex geometry. By using Krasnosel'skii-Guo fixed point theorem and Schauder's fixed point theorem, we derive sufficient conditions for the existence of positive <em>π</em>-periodic solutions to this equation. In addition, we employ numerical bifurcation analysis to explore the dynamical behavior of positive <em>π</em>-periodic solutions.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"452 ","pages":"Article 113776"},"PeriodicalIF":2.3,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145108493","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":"Attractors for second order in time non-conservative dynamics with nonlinear damping","authors":"I. Lasiecka ,&nbsp;J.H. Rodrigues ,&nbsp;M. Roy","doi":"10.1016/j.jde.2025.113760","DOIUrl":"10.1016/j.jde.2025.113760","url":null,"abstract":"<div><div>A long-time behavior of solutions to a nonlinear plate model subject to non-conservative and non-dissipative effects and nonlinear damping is considered. The model under study is a prototype for a suspension bridge under the effects of unstable flow of gas. To counteract the unwanted oscillations a damping mechanism of a nonlinear nature is applied. From the point of view of nonlinear PDEs, we are dealing with a non-dissipative and nonlinear second order in time dynamical system of hyperbolic nature subjected to nonlinear damping. One of the first goals is to establish <em>ultimate dissipativity</em> of all solutions, which will imply an existence of a <em>weak attractor</em>. The combined effects of non-dissipative forcing with nonlinear damping-leading to an overdamping-give rise to major challenges in proving an existence of an absorbing set. Known methods based on equipartition of the energy do not suffice. A rather general novel methodology based on “barrier's” method will be developed to address this and related problems. Ultimately, it will be shown that a weak attractor becomes strong, and the nonlinear PDE system has a coherent finite-dimensional asymptotic behavior.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"451 ","pages":"Article 113760"},"PeriodicalIF":2.3,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145061204","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":"Stable solutions to the Maxwell-Chern-Simons model","authors":"Soojung Kim ,&nbsp;Youngae Lee ,&nbsp;Juhee Sohn","doi":"10.1016/j.jde.2025.113762","DOIUrl":"10.1016/j.jde.2025.113762","url":null,"abstract":"<div><div>In this paper, we consider an elliptic system arising from the study of the Maxwell-Chern-Simons model, which involves two distinct parameters: the Chern-Simons mass scale <em>μ</em> and the inverse Chern-Simons parameter <em>λ</em>. We first establish the equivalence between stable solutions and topological solutions with respect to the two distinct parameters in the Chern-Simon type regime. To address stability of our elliptic system, we study a reduced functional involving the Laplacian, and biharmonic terms appear in the corresponding linearized operator of the second Fréchet derivative. So, meticulous analysis is required to handle the biharmonic terms as well as the disparate scales of the two parameters. Furthermore, we show the uniqueness of stable solutions in the Chern-Simon type regime.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"451 ","pages":"Article 113762"},"PeriodicalIF":2.3,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046535","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 well-posedness of the compressible electrically conducting viscoelastic fluids subject to the Coulomb force in the half space","authors":"Rong Shen,&nbsp;Yong Wang","doi":"10.1016/j.jde.2025.113766","DOIUrl":"10.1016/j.jde.2025.113766","url":null,"abstract":"<div><div>We study the compressible elastic Navier-Stokes-Poisson equations in the three-dimensional upper half space, which describe the dynamics of some kind of compressible electrically conducting viscoelastic fluids subject to the Coulomb force. Under the Hodge boundary condition for the velocity and the Neumann boundary condition for the electrostatic potential, we obtain the unique global solution near a constant equilibrium state in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> space by a delicate energy method. To capture the loss of boundary information for the deformation gradient, we propose the Hodge boundary condition for the deformation which can be preserved over time. Moreover, we use the effective electric field instead of the original one which is proved to have a regularization effect for unbounded problems.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"451 ","pages":"Article 113766"},"PeriodicalIF":2.3,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046533","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":"Sobolev regularity theory for stochastic reaction-diffusion-advection equations with spatially homogeneous colored noises and infinitesimal generators of subordinate Brownian motions","authors":"Jae-Hwan Choi ,&nbsp;Beom-Seok Han ,&nbsp;Daehan Park","doi":"10.1016/j.jde.2025.113761","DOIUrl":"10.1016/j.jde.2025.113761","url":null,"abstract":"<div><div>This article investigates the existence, uniqueness, and regularity of solutions to nonlinear stochastic reaction-diffusion-advection equations (SRDAEs) with spatially homogeneous colored noises and infinitesimal generators of subordinate Brownian motions in mixed norm <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>)</mo></math></span>-spaces. We introduce a new condition—strongly reinforced Dalang's condition—on colored noise, which facilitates a deeper understanding of the complicated relation between nonlinearities and stochastic forces. Additionally, we establish the space-time Hölder type regularity of solutions.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"451 ","pages":"Article 113761"},"PeriodicalIF":2.3,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046531","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 stationary magneto-convective motion of compressible full MHD equations in an infinite horizontal layer","authors":"Rachid Benabidallah ,&nbsp;François Ebobisse ,&nbsp;Mohamed Azouz","doi":"10.1016/j.jde.2025.113744","DOIUrl":"10.1016/j.jde.2025.113744","url":null,"abstract":"<div><div>In an infinite horizontal layer, we consider the equations of the viscous, compressible, and heat conducting magnetohydrodynamic steady flows subject to the gravitational force and to a large gradient of the temperature across the layer. As boundary conditions, we assume in the vertical directions, slip-boundary for the velocity and vertical conditions for magnetic field. The existence of a stationary solution in a small neighborhood of a steady profile close to the rest state is obtained in the Sobolev spaces as limit of a sequence of fixed points of some operators constructed from a suitable linearization of the full magnetohydrodynamic system of equations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"451 ","pages":"Article 113744"},"PeriodicalIF":2.3,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046534","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 critical behavior for the semilinear biharmonic heat equation with forcing term in exterior domain","authors":"Nurdaulet N. Tobakhanov ,&nbsp;Berikbol T. Torebek","doi":"10.1016/j.jde.2025.113758","DOIUrl":"10.1016/j.jde.2025.113758","url":null,"abstract":"<div><div>In this paper, we investigate the critical behavior of solutions to the semilinear biharmonic heat equation with forcing term <span><math><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span>, under six homogeneous boundary conditions. This paper is the first since the seminal work by Bandle et al. (2000) <span><span>[24]</span></span>, to focus on the study of critical exponents in exterior problems for semilinear parabolic equations with a forcing term. By employing a method of test functions and comparison principle, we derive the critical exponents <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>C</mi><mi>r</mi><mi>i</mi><mi>t</mi></mrow></msub></math></span> in the sense of Fujita. Moreover, we show that <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>C</mi><mi>r</mi><mi>i</mi><mi>t</mi></mrow></msub><mo>=</mo><mo>∞</mo></math></span> if <span><math><mi>N</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn></math></span> and <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>C</mi><mi>r</mi><mi>i</mi><mi>t</mi></mrow></msub><mo>=</mo><mfrac><mrow><mi>N</mi></mrow><mrow><mi>N</mi><mo>−</mo><mn>4</mn></mrow></mfrac></math></span> if <span><math><mi>N</mi><mo>⩾</mo><mn>5</mn></math></span>. The impact of the forcing term on the critical behavior of the problem is also of interest, and thus a second critical exponent in the sense of Lee-Ni, depending on the forcing term is introduced. We also discuss the case <span><math><mi>f</mi><mo>≡</mo><mn>0</mn></math></span>, and present the finite-time blow-up results and lifespan estimates of solutions for the subcritical and critical cases. The lifespan estimates of solutions are obtained by employing the method proposed by Ikeda and Sobajama (2019) <span><span>[13]</span></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"451 ","pages":"Article 113758"},"PeriodicalIF":2.3,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046532","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 results for coupled parabolic systems with general sources and some extensions involving degenerate coefficients","authors":"Brandon Carhuas-Torre ,&nbsp;Ricardo Castillo ,&nbsp;Kerven Cea ,&nbsp;Ricardo Freire ,&nbsp;Alex Lira ,&nbsp;Miguel Loayza","doi":"10.1016/j.jde.2025.113765","DOIUrl":"10.1016/j.jde.2025.113765","url":null,"abstract":"<div><div>This work presents optimal conditions for the existence of global solutions for the coupled parabolic system: <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>=</mo><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo><mi>f</mi><mo>(</mo><mi>v</mi><mo>)</mo></math></span> and <span><math><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>−</mo><mi>Δ</mi><mi>v</mi><mo>=</mo><mi>l</mi><mo>(</mo><mi>t</mi><mo>)</mo><mi>g</mi><mo>(</mo><mi>u</mi><mo>)</mo></math></span> in <span><math><mi>Ω</mi><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>)</mo></math></span> with the Dirichlet boundary conditions. Here, <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> is a bounded or unbounded domain, the initial data belong to <span><math><msup><mrow><mo>[</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>Ω</mi><mo>)</mo><mo>]</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span>, and the functions <span><math><mi>f</mi><mo>,</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>,</mo><mi>l</mi><mo>∈</mo><mi>C</mi><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math></span>. We also study the coupled parabolic system with degenerate coefficients: <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>−</mo><mi>div</mi><mo>(</mo><mi>ω</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>∇</mi><mi>u</mi><mo>)</mo><mo>=</mo><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo><mi>f</mi><mo>(</mo><mi>v</mi><mo>)</mo></math></span> and <span><math><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>−</mo><mi>div</mi><mo>(</mo><mi>ω</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>∇</mi><mi>v</mi><mo>)</mo><mo>=</mo><mi>l</mi><mo>(</mo><mi>t</mi><mo>)</mo><mi>g</mi><mo>(</mo><mi>u</mi><mo>)</mo></math></span> in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>)</mo></math></span>, where <em>ω</em> belong to the class <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> of Muckenhoupt functions and may exhibit singularities along the line <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn></math></span>. This problem is related to the fractional Laplacian through the Caffarelli-Silvestre extension given in <span><span>[2]</span></span>. In addition, critical Fujita-type exponents are derived for both systems.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"451 ","pages":"Article 113765"},"PeriodicalIF":2.3,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046530","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 boundedness of almost-periodic oscillators with asymmetric potentials via normal form theorem","authors":"Shuyi Wang,&nbsp;Min Li,&nbsp;Daxiong Piao","doi":"10.1016/j.jde.2025.113763","DOIUrl":"10.1016/j.jde.2025.113763","url":null,"abstract":"<div><div>This paper investigates the boundedness of solutions for the semilinear asymmetric oscillator<span><span><span><math><mrow><mover><mrow><mi>x</mi></mrow><mrow><mo>¨</mo></mrow></mover><mo>+</mo><mi>a</mi><msup><mrow><mi>x</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>−</mo><mi>b</mi><msup><mrow><mi>x</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>=</mo><mi>p</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>,</mo></mrow></math></span></span></span> where <em>p</em> is real analytic and almost-periodic function with infinitely many rationally independent frequencies. A key contribution is the development of a novel normal form theorem for planar almost-periodic mappings under a weighted Diophantine-type nonresonance condition <span><span>(1.7)</span></span>. Unlike prior approaches relying on twist conditions or spatial averaging, our framework eliminates geometric constraints by leveraging the spatial structure of infinite-dimensional frequencies. As a direct consequence, we prove two main results: 1. The existence of infinitely many almost-periodic solutions; 2. The boundedness of all solutions for the asymmetric oscillator, even when traditional twist integrals (e.g., <span><span>(1.5)</span></span>) vanish. This work unifies periodic/quasi-periodic boundedness theories and extends them to the almost-periodic regime, resolving long-standing limitations in planar Hamiltonian systems with asymmetric potentials.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"451 ","pages":"Article 113763"},"PeriodicalIF":2.3,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145027285","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":"Bifurcation of gravity-capillary Stokes waves with constant vorticity","authors":"T. Barbieri ,&nbsp;M. Berti ,&nbsp;A. Maspero ,&nbsp;M. Mazzucchelli","doi":"10.1016/j.jde.2025.113753","DOIUrl":"10.1016/j.jde.2025.113753","url":null,"abstract":"<div><div>We consider the gravity-capillary water waves equations of a 2D fluid with constant vorticity. By employing variational methods we prove the bifurcation of periodic traveling water waves –which are steady in a moving frame– for <em>all</em> the values of gravity, surface tension, constant vorticity, depth and wavelenght, extending previous results valid for restricted values of the parameters. We parametrize the bifurcating Stokes waves either with their speed or their momentum.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"451 ","pages":"Article 113753"},"PeriodicalIF":2.3,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020204","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}