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On length-preserving and area-preserving inverse curvature flow of planar curves with singularities 具有奇异点的平面曲线的保长保面积逆曲率流
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-06-10 DOI: 10.1016/j.jde.2025.113517
Yunlong Yang , Yanwen Zhao , Jianbo Fang , Yanlong Zhang
{"title":"On length-preserving and area-preserving inverse curvature flow of planar curves with singularities","authors":"Yunlong Yang ,&nbsp;Yanwen Zhao ,&nbsp;Jianbo Fang ,&nbsp;Yanlong Zhang","doi":"10.1016/j.jde.2025.113517","DOIUrl":"10.1016/j.jde.2025.113517","url":null,"abstract":"<div><div>This paper aims to investigate the evolution problem for planar curves with singularities. Motivated by the inverse curvature flow introduced by Li and Wang (2023) <span><span>[33]</span></span>, we intend to consider the area-preserving and length-preserving inverse curvature flow with nonlocal term for <em>ℓ</em>-convex Legendre curves. For the area-preserving flow, an <em>ℓ</em>-convex Legendre curve with initial algebraic area <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&gt;</mo><mn>0</mn></math></span> evolves to a circle of radius <span><math><msqrt><mrow><mfrac><mrow><msub><mrow><mi>A</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow><mrow><mi>π</mi></mrow></mfrac></mrow></msqrt></math></span>. For the length-preserving flow, an <em>ℓ</em>-convex Legendre curve with initial algebraic length <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> evolves to a circle of radius <span><math><mfrac><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow><mrow><mn>2</mn><mi>π</mi></mrow></mfrac></math></span>. As the by-product, we obtain some geometric inequalities for <em>ℓ</em>-convex Legendre curves through the length-preserving flow.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"443 ","pages":"Article 113517"},"PeriodicalIF":2.4,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144241005","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}
引用次数: 0
KAM theorem for degenerate generalized Hamiltonian systems with continuous parameters 连续参数退化广义哈密顿系统的KAM定理
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-06-10 DOI: 10.1016/j.jde.2025.113504
Jiayin Du , Shuguan Ji , Yong Li
{"title":"KAM theorem for degenerate generalized Hamiltonian systems with continuous parameters","authors":"Jiayin Du ,&nbsp;Shuguan Ji ,&nbsp;Yong Li","doi":"10.1016/j.jde.2025.113504","DOIUrl":"10.1016/j.jde.2025.113504","url":null,"abstract":"<div><div>In this paper, we prove the persistence of invariant tori for degenerate generalized Hamiltonian systems with continuous parameters. We demonstrate that the persistent invariant tori retain the same frequency as the unperturbed tori under a certain transversality condition and a weak convexity condition for the frequency mapping. Generally speaking, at least Lipschitz continuity with respect to the parameter is needed in KAM-type results, while in this paper, we only require it to be continuous. Additionally, the system we consider is degenerate. Therefore, this paper can also be seen as an extension of KAM-type theory from non-degenerate generalized Hamiltonian systems to degenerate generalized Hamiltonian systems.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"441 ","pages":"Article 113504"},"PeriodicalIF":2.4,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144254784","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}
引用次数: 0
Accelerating or not in the spatial propagation of nonlocal dispersal cooperative reducible systems 非局部分散合作可约系统的空间传播加速或不加速
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-06-10 DOI: 10.1016/j.jde.2025.113519
Teng-Long Cui , Wan-Tong Li , Wen-Bing Xu
{"title":"Accelerating or not in the spatial propagation of nonlocal dispersal cooperative reducible systems","authors":"Teng-Long Cui ,&nbsp;Wan-Tong Li ,&nbsp;Wen-Bing Xu","doi":"10.1016/j.jde.2025.113519","DOIUrl":"10.1016/j.jde.2025.113519","url":null,"abstract":"<div><div>This paper investigates the spatial propagation problem in cooperative recursive systems in the absence of irreducibility, which is a critical assumption to guarantee uniform spatial propagation across all components. When the linearization at zero vector of the reducible system is in Frobenius form, we demonstrate that the <em>i</em>-th component exhibiting accelerated propagation could accelerate the spatial propagation of all other components and the spreading speeds of all components are infinite, provided that the <span><math><mo>(</mo><mi>i</mi><mo>,</mo><mi>i</mi><mo>)</mo></math></span>-entry in the Frobenius matrix belongs to the first diagonal block. This result reveals that uniform propagation of all components can occur even when the irreducibility condition is not satisfied. However, when the <span><math><mo>(</mo><mi>i</mi><mo>,</mo><mi>i</mi><mo>)</mo></math></span>-entry is not in the first diagonal block, some components have finite spreading speeds while others have infinite ones, which implies that the propagation of the system is non-uniform. Moreover, we extend our analysis to nonlocal dispersal cooperative systems and explore a special case where the dispersal kernel of a component has an algebraically decaying tail.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"443 ","pages":"Article 113519"},"PeriodicalIF":2.4,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144241194","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}
引用次数: 0
Wellposedness, equilibria, and patterns of an epidemic PDE model with spatiotemporally nonlocal memory 具有时空非局部记忆的流行病PDE模型的适位性、平衡和模式
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-06-09 DOI: 10.1016/j.jde.2025.113491
Guodong Liu , Hao Wang , Xiaoyan Zhang
{"title":"Wellposedness, equilibria, and patterns of an epidemic PDE model with spatiotemporally nonlocal memory","authors":"Guodong Liu ,&nbsp;Hao Wang ,&nbsp;Xiaoyan Zhang","doi":"10.1016/j.jde.2025.113491","DOIUrl":"10.1016/j.jde.2025.113491","url":null,"abstract":"<div><div>Spatiotemporal memory is incorporated to describe the movement of susceptible individuals in an epidemic reaction-diffusion model with vaccination. We propose equivalent quasilinear parabolic systems for the fully nonlinear PDE model to address global solvability. Theoretical analysis verifies that the solution remains bounded in a one-dimensional domain and can be extended to a three-dimensional domain by restricting the memory-driven diffusion rate. Furthermore, we discuss the existence and multiplicity of equilibria for the model with the zero memory-driven movement rate. Numerical findings reveal that spatiotemporal memory of susceptible individuals contributes to periodically reducing infection, given the formation of memory-driven temporal patterns.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"442 ","pages":"Article 113491"},"PeriodicalIF":2.4,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144239535","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}
引用次数: 0
The compressible Euler-Poisson limit to the Vlasov-Poisson-Boltzmann system with Fermi-Dirac statistics 费米-狄拉克统计的弗拉索夫-泊松-玻尔兹曼系统的可压缩欧拉-泊松极限
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-06-09 DOI: 10.1016/j.jde.2025.113499
Ning Jiang , Wengang Yang , Kai Zhou
{"title":"The compressible Euler-Poisson limit to the Vlasov-Poisson-Boltzmann system with Fermi-Dirac statistics","authors":"Ning Jiang ,&nbsp;Wengang Yang ,&nbsp;Kai Zhou","doi":"10.1016/j.jde.2025.113499","DOIUrl":"10.1016/j.jde.2025.113499","url":null,"abstract":"<div><div>We justify the compressible Euler-Poisson limit of the quantum Vlasov-Poisson-Boltzmann equations with Fermi-Dirac statistics as the Knudsen number goes to zero. The truncated Hilbert expansion and the classical <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mtext>-</mtext><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> framework are used to derive the validity of the hydrodynamic limits of the quantum Vlasov-Poisson-Boltzmann equations with hard sphere collision kernel. Due to the coupling effects of a self-consistent electric field, the extra <span><math><msup><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>,</mo><mo>∞</mo></mrow></msup></math></span> estimates for some new weighted function are necessary to close the energy.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"442 ","pages":"Article 113499"},"PeriodicalIF":2.4,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144239534","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}
引用次数: 0
Singular solutions of complex vector fields on the Möbius band Möbius波段上复向量场的奇异解
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-06-09 DOI: 10.1016/j.jde.2025.113493
Renato A. Laguna, Sérgio Luís Zani
{"title":"Singular solutions of complex vector fields on the Möbius band","authors":"Renato A. Laguna,&nbsp;Sérgio Luís Zani","doi":"10.1016/j.jde.2025.113493","DOIUrl":"10.1016/j.jde.2025.113493","url":null,"abstract":"<div><div>Let <span><math><mi>M</mi></math></span> be the Möbius band, uniformized as <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>/</mo><mi>G</mi></math></span> where <em>G</em> is the automorphism group generated by the isometry <span><math><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>↦</mo><mo>(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>,</mo><mo>−</mo><mi>y</mi><mo>)</mo></math></span>. We show the existence of singular solutions <em>u</em> to the complex vector field<span><span><span><math><mi>L</mi><mo>≐</mo><mfrac><mrow><mo>∂</mo></mrow><mrow><mo>∂</mo><mi>x</mi></mrow></mfrac><mo>+</mo><mi>y</mi><mo>(</mo><mi>a</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>+</mo><mi>i</mi><mi>b</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>)</mo><mfrac><mrow><mo>∂</mo></mrow><mrow><mo>∂</mo><mi>y</mi></mrow></mfrac><mo>,</mo><mspace></mspace><mi>a</mi><mo>,</mo><mi>b</mi><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>;</mo><mi>R</mi><mo>)</mo></math></span></span></span> where both <em>L</em> and <em>u</em> pass to the quotient. In other words, the passage of <em>L</em> to the Möbius band is not globally hypoelliptic. Some consequences for the question of whether non-orientable surfaces admit globally hypoelliptic vector fields are examined.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"442 ","pages":"Article 113493"},"PeriodicalIF":2.4,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144239536","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}
引用次数: 0
Well-posedness and strong attractors for a beam model with degenerate nonlocal strong damping 简并非局部强阻尼梁模型的适位性和强吸引子
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-06-09 DOI: 10.1016/j.jde.2025.113495
Senlin Yan , Chengkui Zhong
{"title":"Well-posedness and strong attractors for a beam model with degenerate nonlocal strong damping","authors":"Senlin Yan ,&nbsp;Chengkui Zhong","doi":"10.1016/j.jde.2025.113495","DOIUrl":"10.1016/j.jde.2025.113495","url":null,"abstract":"<div><div>This paper is devoted to initial-boundary value problem of an extensible beam equation with degenerate nonlocal energy damping in <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>: <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi><mi>t</mi></mrow></msub><mo>−</mo><mi>κ</mi><mi>Δ</mi><mi>u</mi><mo>+</mo><msup><mrow><mi>Δ</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>−</mo><mi>γ</mi><msup><mrow><mo>(</mo><msup><mrow><mo>‖</mo><mi>Δ</mi><mi>u</mi><mo>‖</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mo>‖</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>‖</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mi>q</mi></mrow></msup><mi>Δ</mi><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><mi>f</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></span>. We prove the global existence, regularity and uniqueness of weak solutions. Moreover, we establish the existence of a strong attractor for the corresponding weak solution semigroup, where the “strong” means that the compactness and attractiveness of the attractor are in the topology of a stronger space <span><math><msub><mrow><mi>H</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>q</mi></mrow></mfrac></mrow></msub></math></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"442 ","pages":"Article 113495"},"PeriodicalIF":2.4,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144239537","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}
引用次数: 0
Construction of weak solutions to the equations of a compressible viscous model 可压缩粘性模型方程弱解的构造
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-06-06 DOI: 10.1016/j.jde.2025.113484
Nilasis Chaudhuri , Piotr B. Mucha , Milan Pokorný
{"title":"Construction of weak solutions to the equations of a compressible viscous model","authors":"Nilasis Chaudhuri ,&nbsp;Piotr B. Mucha ,&nbsp;Milan Pokorný","doi":"10.1016/j.jde.2025.113484","DOIUrl":"10.1016/j.jde.2025.113484","url":null,"abstract":"<div><div>The paper aims on the construction of weak solutions to equations of a model of compressible viscous fluids, being a simplification of the classical compressible Navier-Stokes system. We present a novel scheme for approximating systems that preserves structural integrity by avoiding classical regularization with <span><math><mo>−</mo><mi>ϵ</mi><mi>Δ</mi><mi>ϱ</mi></math></span>, thus maintaining the transport character of the continuity equation. Our approach, which necessitates specific conditions on the constitutive equation, accommodates physically relevant models such as isentropic and van der Waals gases, and globally handles non-monotone pressures. From an analytical perspective, our method synthesizes techniques from Feireisl–Lions and Bresch–Jabin to demonstrate the convergence of approximate densities using compensated compactness techniques. We also apply renormalization of the continuity equations and utilize weight techniques to manage unfavorable terms.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"441 ","pages":"Article 113484"},"PeriodicalIF":2.4,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144222952","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}
引用次数: 0
On the variational principle for a class of skew product transformations 一类斜积变换的变分原理
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-06-06 DOI: 10.1016/j.jde.2025.113498
Nian Liu , Xue Liu
{"title":"On the variational principle for a class of skew product transformations","authors":"Nian Liu ,&nbsp;Xue Liu","doi":"10.1016/j.jde.2025.113498","DOIUrl":"10.1016/j.jde.2025.113498","url":null,"abstract":"<div><div>In this paper, we establish a variational principle, between the fiber Bowen's topological entropy on conditional level sets of Birkhoff average and fiber measure-theoretical entropy, for the skew product transformation driven by a uniquely ergodic homeomorphism system satisfying Anosov and topological mixing on fibers property. We prove it by utilizing a fiber specification property. Moreover, we prove that such skew product transformation has specification property defined by Gundlach and Kifer <span><span>[16]</span></span>. Employing their main results, every Hölder continuous potential has a unique equilibrium state, and we also establish a variational principle between the fiber measure-theoretic entropy and the fiber Bowen's topological entropy on conditional level sets of local entropy for such unique equilibrium state. Examples of systems under consideration are given, such as fiber Anosov maps on 2-dimension tori driven by any irrational rotation on circle, and random composition of 2x2 area preserving positive matrices driven by a uniquely ergodic subshift.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"442 ","pages":"Article 113498"},"PeriodicalIF":2.4,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144230892","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}
引用次数: 0
Vorticity interior trace estimates and higher derivative estimates via blow-up method 用爆破法估计涡度内迹和高导数估计
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-06-06 DOI: 10.1016/j.jde.2025.113486
Jincheng Yang
{"title":"Vorticity interior trace estimates and higher derivative estimates via blow-up method","authors":"Jincheng Yang","doi":"10.1016/j.jde.2025.113486","DOIUrl":"10.1016/j.jde.2025.113486","url":null,"abstract":"<div><div>We derive several nonlinear a priori trace estimates for the 3D incompressible Navier–Stokes equation, which extend the current picture of higher derivative estimates in the mixed norm. The main ingredient is the blow-up method and a novel averaging operator, which could apply to PDEs with scaling invariance and <em>ε</em>-regularity, possibly with a drift.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"442 ","pages":"Article 113486"},"PeriodicalIF":2.4,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144230895","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}
引用次数: 0
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