Journal of Differential Equations最新文献

{"title":"Global bifurcation results for a delay differential system representing a chemostat model","authors":"Pablo Amster ,&nbsp;Pierluigi Benevieri","doi":"10.1016/j.jde.2025.113222","DOIUrl":"10.1016/j.jde.2025.113222","url":null,"abstract":"<div><div>This paper studies a one-species chemostat model described by a system of differential delay equations, featuring a periodic input of a single nutrient with period <em>ω</em>. The delay represents the interval time between the consumption of the nutrient and its metabolization by the microbial species. We obtain global bifurcation results for the periodic solutions with period <em>ω</em>. Our proof is based on the application of the topological degree theory combined with a Whyburn-type Lemma.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"434 ","pages":"Article 113222"},"PeriodicalIF":2.4,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143641155","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":"Existence and regularity results for the penalized thin obstacle problem with variable coefficients","authors":"Donatella Danielli ,&nbsp;Brian Krummel","doi":"10.1016/j.jde.2025.02.084","DOIUrl":"10.1016/j.jde.2025.02.084","url":null,"abstract":"<div><div>In this paper we give a comprehensive treatment of a two-penalty boundary obstacle problem for a divergence form elliptic operator, motivated by applications to fluid dynamics and thermics. Specifically, we prove existence, uniqueness and optimal regularity of solutions, and establish structural properties of the free boundary. The proofs are based on tailor-made monotonicity formulas of Almgren, Weiss, and Monneau-type, combined with the classical theory of oblique derivative problems.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"432 ","pages":"Article 113213"},"PeriodicalIF":2.4,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143643295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hölder regularity for degenerate parabolic double-phase equations","authors":"Wontae Kim ,&nbsp;Kristian Moring ,&nbsp;Lauri Särkiö","doi":"10.1016/j.jde.2025.113231","DOIUrl":"10.1016/j.jde.2025.113231","url":null,"abstract":"<div><div>We prove that bounded weak solutions to degenerate parabolic double-phase equations of <em>p</em>-Laplace type are locally Hölder continuous. The proof is based on phase analysis and methods for the <em>p</em>-Laplace equation. In particular, the phase analysis determines whether the double-phase equation is locally similar to the <em>p</em>-Laplace or the <em>q</em>-Laplace equation.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"434 ","pages":"Article 113231"},"PeriodicalIF":2.4,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quasi-periodic solutions around plane wave of high dimensional nonlinear Schrödinger equation","authors":"Meina Gao ,&nbsp;Jianjun Liu ,&nbsp;Zejing Liu","doi":"10.1016/j.jde.2025.113229","DOIUrl":"10.1016/j.jde.2025.113229","url":null,"abstract":"<div><div>In this paper, a degenerate KAM theorem with multiple normal frequencies is established under qualitative non-degenerate conditions. As an application, quasi-periodic solutions around plane wave are obtained for high dimensional nonlinear Schrödinger equation with periodic boundary conditions.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"434 ","pages":"Article 113229"},"PeriodicalIF":2.4,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143637375","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 time decay rate to one-dimensional two-phase flow model","authors":"Xushan Huang ,&nbsp;Yi Wang","doi":"10.1016/j.jde.2025.02.081","DOIUrl":"10.1016/j.jde.2025.02.081","url":null,"abstract":"<div><div>We investigate the global existence and optimal time decay rate of solution to the one dimensional (1D) two-phase flow described by compressible Euler equations coupled with compressible Navier-Stokes equations through the relaxation drag force on the momentum equations (Euler-Navier-Stokes system). First, we prove the global existence of strong solution and the stability of the constant equilibrium state to 1D Cauchy problem of compressible Euler-Navier-Stokes system by using the standard continuity argument for small <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> data while their second order derivative can be large. Then we derive the optimal time decay rate to the constant equilibrium state. Compared with multi-dimensional case, it is much harder to get optimal time decay rate by direct spectrum method due to a slower convergence rate of the fundamental solution in 1D case. To overcome this main difficulty, we need to first carry out time-weighted energy estimates (not optimal) for higher order derivatives, and based on these time-weighted estimates, we can close a priori assumptions and get the optimal time decay rate by spectrum analysis method. Moreover, due to non-conserved form and insufficient decay rate of the coupled drag force terms between the two-phase flows, we essentially need to use momentum variables <span><math><mo>(</mo><mi>m</mi><mo>=</mo><mi>ρ</mi><mi>u</mi><mo>,</mo><mi>M</mi><mo>=</mo><mi>n</mi><mi>ω</mi><mo>)</mo></math></span>, rather than velocity variables <span><math><mo>(</mo><mi>u</mi><mo>,</mo><mi>ω</mi><mo>)</mo></math></span> in the spectrum analysis, to fully cancel out those non-conserved and insufficient time decay drag force terms.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"433 ","pages":"Article 113210"},"PeriodicalIF":2.4,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143631761","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":"Threshold dynamics for a class of time-delayed nonlocal dispersal equations with a shifting habitat","authors":"Jing Chen ,&nbsp;Leyi Jiang ,&nbsp;Taishan Yi","doi":"10.1016/j.jde.2025.113228","DOIUrl":"10.1016/j.jde.2025.113228","url":null,"abstract":"<div><div>This paper is devoted to the study of the threshold dynamics for a class of time-delayed nonlocal dispersal equations with a shifting habitat which is suitable for survival only in bounded regions. We first establish the asymptotic annihilation of solutions under several appropriate assumptions. In order to avoid the tedious asymptotic spectral radius analysis of the solution map without compactness, we then transform the issues corresponding to forced wave for the original system into a fixed point problem of traveling wave map. Notably, such traveling wave map possesses compactness, enabling us to establish the existence and uniqueness of fixed points in terms of asymptotic spectral radius. Finally, these, together with the theory of asymptotic spectral radius again, yield the threshold dynamics of the original system.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"433 ","pages":"Article 113228"},"PeriodicalIF":2.4,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143631762","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":"Persistence of a class of degenerate hyperbolic lower dimensional invariant tori in Hamiltonian systems","authors":"Qi Li ,&nbsp;Junxiang Xu","doi":"10.1016/j.jde.2025.113227","DOIUrl":"10.1016/j.jde.2025.113227","url":null,"abstract":"<div><div>This paper proves the persistence of degenerate hyperbolic lower dimensional invariant tori under small perturbations. The result is an extension of that in <span><span>[41]</span></span> to multiple dimensional case. The proof is based on the KAM technique with external parameters as counter terms and the theory of Brouwer degree.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"433 ","pages":"Article 113227"},"PeriodicalIF":2.4,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143619433","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 and scattering of the two dimensional cubic focusing nonlinear Schrödinger system","authors":"Xing Cheng ,&nbsp;Zihua Guo ,&nbsp;Gyeongha Hwang ,&nbsp;Haewon Yoon","doi":"10.1016/j.jde.2025.113225","DOIUrl":"10.1016/j.jde.2025.113225","url":null,"abstract":"<div><div>In this article, we prove the global well-posedness (GWP) and scattering of the cubic focusing infinitely coupled nonlinear Schrödinger system (NLSS) on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> below the ground state in <span><math><msubsup><mrow><mi>L</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msubsup><msup><mrow><mi>h</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><mi>Z</mi><mo>)</mo></math></span>. We first establish the variational characterization of the ground state and derive the threshold for global well-posedness and scattering. We then demonstrate the global well-posedness and scattering below the threshold using the concentration-compactness/rigidity method. The almost periodic solution is excluded by adapting the argument used in the proof of the focusing mass-critical nonlinear Schrödinger equations (NLS) by B. Dodson. As a byproduct of the scattering of the cubic focusing infinitely coupled nonlinear Schrödinger system, we obtain the scattering of the cubic focusing nonlinear Schrödinger equation on the small cylinder. We also show the global well-posedness and scattering of the two dimensional <em>N</em>-coupled focusing cubic nonlinear Schrödinger system in <span><math><msup><mrow><mo>(</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>)</mo></mrow><mrow><mi>N</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"433 ","pages":"Article 113225"},"PeriodicalIF":2.4,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143619349","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":"Universal log-gradient estimates of solutions to Δpv + bvq + cvr = 0 on manifolds and applications","authors":"Jie He ,&nbsp;Yuanqing Ma ,&nbsp;Youde Wang","doi":"10.1016/j.jde.2025.113233","DOIUrl":"10.1016/j.jde.2025.113233","url":null,"abstract":"<div><div>In this paper, we employ Cheng-Yau's method, the Saloff-Coste's Sobolev inequalities and Nash-Moser iteration to study local and global properties of positive solutions to the equation<span><span><span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>p</mi></mrow></msub><mi>v</mi><mo>+</mo><mi>b</mi><msup><mrow><mi>v</mi></mrow><mrow><mi>q</mi></mrow></msup><mo>+</mo><mi>c</mi><msup><mrow><mi>v</mi></mrow><mrow><mi>r</mi></mrow></msup><mo>=</mo><mn>0</mn></math></span></span></span> on complete Riemannian manifolds with Ricci curvature bounded from below, where <span><math><mi>b</mi><mo>,</mo><mi>c</mi><mo>∈</mo><mi>R</mi></math></span>, <span><math><mi>p</mi><mo>&gt;</mo><mn>1</mn></math></span>, and <span><math><mi>q</mi><mo>≤</mo><mi>r</mi></math></span> are some real constants. Assuming certain conditions on <span><math><mi>b</mi><mo>,</mo><mspace></mspace><mi>c</mi><mo>,</mo><mspace></mspace><mi>p</mi><mo>,</mo><mspace></mspace><mi>q</mi></math></span> and <em>r</em>, we derive succinct and universal Cheng-Yau type gradient estimates for positive solutions, which are of sharp form. These gradient estimates allow us to obtain some Liouville-type theorems and Harnack inequalities. Our Liouville-type results are novel even in Euclidean spaces. Based on the global gradient estimates obtained, we also obtain the explicit global gradient estimates for such entire solutions by a lemma of Sung and Wang. As applications, we show the uniqueness of positive solutions to some generalized Allen-Cahn equation and Fisher-KPP equations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"434 ","pages":"Article 113233"},"PeriodicalIF":2.4,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143621041","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":"Growth of Sobolev norms for completely resonant quantum harmonic oscillators on R2","authors":"Beatrice Langella,&nbsp;Alberto Maspero,&nbsp;Maria Teresa Rotolo","doi":"10.1016/j.jde.2025.113221","DOIUrl":"10.1016/j.jde.2025.113221","url":null,"abstract":"<div><div>We consider time dependently perturbed quantum harmonic oscillators in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>:<span><span><span><math><mi>i</mi><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>(</mo><mo>−</mo><msubsup><mrow><mo>∂</mo></mrow><mrow><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mrow><mn>2</mn></mrow></msubsup><mo>−</mo><msubsup><mrow><mo>∂</mo></mrow><mrow><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow><mrow><mn>2</mn></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>)</mo><mi>u</mi><mo>+</mo><mi>V</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>D</mi><mo>)</mo><mi>u</mi><mo>,</mo><mspace></mspace><mspace></mspace><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo></math></span></span></span> where <span><math><mi>V</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>D</mi><mo>)</mo></math></span> is a selfadjoint pseudodifferential operator of degree zero, 2<em>π</em> periodic in time.</div><div>We identify sufficient conditions on the principal symbol of the potential <span><math><mi>V</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>D</mi><mo>)</mo></math></span> that ensure existence of solutions exhibiting unbounded growth in time of their positive Sobolev norms and we show that the class of symbols satisfying such conditions is generic in the Fréchet space of classical 2<em>π</em>-time periodic symbols of order zero. To prove our result we apply the abstract Theorem of <span><span>[46]</span></span>: the main difficulty is to find a conjugate operator <em>A</em> for the resonant average of <span><math><mi>V</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>D</mi><mo>)</mo></math></span>. We construct explicitly the symbol of the conjugate operator <em>A</em>, called escape function, combining techniques from microlocal analysis, dynamical systems and contact topology.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"433 ","pages":"Article 113221"},"PeriodicalIF":2.4,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143609221","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}