Journal of Differential Equations最新文献_第5页

Suppression of blow-up in Patlak-Keller-Segel-Navier-Stokes system via the Poiseuille flow

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-04-11 DOI: 10.1016/j.jde.2025.113301

Hao Li , Zhaoyin Xiang , Xiaoqian Xu

引用次数: 0

Stability for the Sobolev inequality in cones

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-04-11 DOI: 10.1016/j.jde.2025.113325

Giulio Ciraolo , Filomena Pacella , Camilla Chiara Polvara

引用次数: 0

Mathematical modeling and analysis for the chemotactic diffusion in porous media with incompressible Navier-Stokes equations over bounded domain

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-04-11 DOI: 10.1016/j.jde.2025.113305

Fugui Ma , Wenyi Tian , Weihua Deng

{"title":"Mathematical modeling and analysis for the chemotactic diffusion in porous media with incompressible Navier-Stokes equations over bounded domain","authors":"Fugui Ma , Wenyi Tian , Weihua Deng","doi":"10.1016/j.jde.2025.113305","DOIUrl":"10.1016/j.jde.2025.113305","url":null,"abstract":"<div><div>Considering soil as a porous medium, the biological mechanism and dynamic behavior of myxobacteria and slime affected by favorable environments in the soil cannot be well characterized by the classical Keller-Segel-Navier-Stokes equations. In this work, we employ the continuous time random walk (CTRW) approach to characterize the diffusion behavior of myxobacteria and slime in porous media at the microscale, and develop a new macroscopic model named as the time-fractional Keller-Segel system. Then it is coupled with the incompressible Navier-Stokes equations through transport and buoyancy, resulting in the TF-KSNS system, which appropriately describes the chemotactic diffusion of myxobacteria and slime in the soil. In addition, we demonstrate that the TF-KSNS system associated with initial and no-flux/no-flux/Dirichlet boundary conditions over a smoothly bounded domain in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> (<span><math><mi>d</mi><mo>≥</mo><mn>2</mn></math></span>) admits a local well-posed mild solution, which continuously depends on the initial data. Moreover, the blow-up of the mild solution is rigorously investigated.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"436 ","pages":"Article 113305"},"PeriodicalIF":2.4,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143816367","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

Existence and asymptotic stability of a generic Lotka-Volterra system with nonlinear spatially heterogeneous cross-diffusion

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-04-11 DOI: 10.1016/j.jde.2025.113302

Tian Xu Wang , Jiwoon Sim , Hao Wang

{"title":"Existence and asymptotic stability of a generic Lotka-Volterra system with nonlinear spatially heterogeneous cross-diffusion","authors":"Tian Xu Wang , Jiwoon Sim , Hao Wang","doi":"10.1016/j.jde.2025.113302","DOIUrl":"10.1016/j.jde.2025.113302","url":null,"abstract":"<div><div>This article considers a class of Lotka-Volterra systems with multiple nonlinear cross-diffusion, commonly known as prey-taxis models. The existence and stability of classic solutions for such systems with spatially homogeneous sources and taxis have been studied in one- or two-dimensional space, however, the proof is non-trivial for a more general setting with spatially heterogeneous predation functions and taxis coefficient functions in arbitrary dimensions. This study introduces a new weighted <span><math><msubsup><mrow><mi>L</mi></mrow><mrow><mi>ϵ</mi></mrow><mrow><mi>p</mi></mrow></msubsup></math></span>-norm and extends some classical inequalities within this normed space. Coupled energy estimates are employed to establish initial bounds, followed by applying heat kernel properties and an advanced bootstrap process to enhance solution regularity. For stability analysis, we extend LaSalle's invariance principle to a general <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> setting and utilize it alongside Lyapunov functions to analyze the stability of each possible constant equilibrium. All results are achieved without introducing an extra logistic growth term for predators or imposing smallness conditions on taxis coefficients.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"434 ","pages":"Article 113302"},"PeriodicalIF":2.4,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143815983","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

Approximation of the first Steklov–Dirichlet eigenvalue on eccentric spherical shells in general dimensions

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-04-11 DOI: 10.1016/j.jde.2025.113295

Jiho Hong , Woojoo Lee , Mikyoung Lim

{"title":"Approximation of the first Steklov–Dirichlet eigenvalue on eccentric spherical shells in general dimensions","authors":"Jiho Hong , Woojoo Lee , Mikyoung Lim","doi":"10.1016/j.jde.2025.113295","DOIUrl":"10.1016/j.jde.2025.113295","url":null,"abstract":"<div><div>We study the first Steklov–Dirichlet eigenvalue on eccentric spherical shells in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow></msup></math></span> with <span><math><mi>n</mi><mo>≥</mo><mn>1</mn></math></span>, imposing the Steklov condition on the outer boundary sphere, denoted by <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>S</mi></mrow></msub></math></span>, and the Dirichlet condition on the inner boundary sphere. The first eigenfunction admits a Fourier–Gegenbauer series expansion via the bispherical coordinates, where the Dirichlet-to-Neumann operator on <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>S</mi></mrow></msub></math></span> can be recursively expressed in terms of the expansion coefficients <span><span>[1]</span></span>. In this paper, we develop a finite section approach for the Dirichlet-to-Neumann operator to approximate the first Steklov–Dirichlet eigenvalue on eccentric spherical shells. We prove the exponential convergence of this approach by using the variational characterization of the first eigenvalue. Furthermore, based on the convergence result, we propose a numerical computation scheme as an extension of the two-dimensional result in <span><span>[2]</span></span> to general dimensions. We provide numerical examples of the first Steklov–Dirichlet eigenvalue on eccentric spherical shells with various geometric configurations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"437 ","pages":"Article 113295"},"PeriodicalIF":2.4,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143815582","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

Global dynamics of a degenerate reaction-diffusion model for Brucellosis transmission

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-04-11 DOI: 10.1016/j.jde.2025.113284

Shu-Min Liu , Shi Zhao , Zhenguo Bai , Yijun Lou , Gui-Quan Sun , Li Li

{"title":"Global dynamics of a degenerate reaction-diffusion model for Brucellosis transmission","authors":"Shu-Min Liu , Shi Zhao , Zhenguo Bai , Yijun Lou , Gui-Quan Sun , Li Li","doi":"10.1016/j.jde.2025.113284","DOIUrl":"10.1016/j.jde.2025.113284","url":null,"abstract":"<div><div>The effective control of brucellosis is critically important for global public health and the economy. This paper presents a novel degenerate reaction-diffusion model for brucellosis, incorporating spatiotemporal heterogeneity, human behavior dynamics and a multi-stage latent period. The well-posedness of the model is rigorously analyzed, and the basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is derived via the next-generation operator method. A threshold result based on the <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is established: global asymptotic stability of the disease-free equilibrium is proven for <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo><</mo><mn>1</mn></math></span>, while disease persistence is rigorously demonstrated for <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>></mo><mn>1</mn></math></span>. The global asymptotic stability of the disease-free equilibrium for <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mn>1</mn></math></span> is further proven under spatial heterogeneity. Furthermore, the global attractiveness of the endemic equilibrium under spatiotemporal homogeneity is established through the construction of a Lyapunov function. Numerical simulations identify critical drivers of brucellosis transmission, including human behavior adaptation, latent period staging, and grazing intensity, providing significant insights for brucellosis control strategies.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"437 ","pages":"Article 113284"},"PeriodicalIF":2.4,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143815710","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

Canard explosion in Filippov system with a cusp-fold singularity via regularization

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-04-11 DOI: 10.1016/j.jde.2025.113294

Hongyi Xie , Yuhua Cai , Jianhe Shen

{"title":"Canard explosion in Filippov system with a cusp-fold singularity via regularization","authors":"Hongyi Xie , Yuhua Cai , Jianhe Shen","doi":"10.1016/j.jde.2025.113294","DOIUrl":"10.1016/j.jde.2025.113294","url":null,"abstract":"<div><div>In this paper, we reveal the completely dynamical process of canard explosion in planar Filippov system with a cusp-fold singularity via Sotomayor-Teixeira regularization. It is found that the cusp-fold singularity is the organization center responsible for the birth and the death of canard explosion in planar Filippov system. By unfolding the cusp-fold singularity, we obtain a suitable topology in the resulting regularized system to describe canard explosion from small-amplitude cycle via the first supercritical Hopf bifurcation to canard cycle without head, the maximal canard, canard cycle with head, and finally relaxation oscillation happening quickly. In the current setting, the visible-invisible fold-fold singularity and the invisible fold singularity unfolded from the cusp-fold singularity respectively play the roles analogous to the canard point and the jump point in smooth singular perturbation system. After the occurrence of canard explosion, the relaxation oscillation will then disappear via the bifurcation of homoclinic-like connection and the second Hopf bifurcation. All the bifurcation curves are determined explicitly, and all the theoretical findings are verified by numerical experiments.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"436 ","pages":"Article 113294"},"PeriodicalIF":2.4,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143816366","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

Spectral instability of periodic peaked waves in the μ-b-family of Camassa-Holm equations

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-04-11 DOI: 10.1016/j.jde.2025.113311

Haijing Song , Ying Fu , Hao Wang

{"title":"Spectral instability of periodic peaked waves in the μ-b-family of Camassa-Holm equations","authors":"Haijing Song , Ying Fu , Hao Wang","doi":"10.1016/j.jde.2025.113311","DOIUrl":"10.1016/j.jde.2025.113311","url":null,"abstract":"<div><div>Considered herein is a <em>μ</em>-version <em>b</em>-family of the Camassa-Holm equations on the circle. First, we define a linearized operator associated with these equations in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mi>S</mi><mo>)</mo><mo>∩</mo><msup><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>,</mo><mo>∞</mo></mrow></msup><mo>(</mo><mi>S</mi><mo>)</mo></math></span> and extend its domain to the larger space <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>S</mi><mo>)</mo></math></span>. Then we show that the periodic peaked waves of these equations are spectrally unstable in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>S</mi><mo>)</mo></math></span> for <span><math><mi>b</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn></math></span>. Finally, by using the method of characteristic, the time evolution of the linearized system is obtained, which is related to the spectral properties of the linearized operator in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>S</mi><mo>)</mo></math></span>. We emphasize that this is the first result which proves the spectral instability in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mrow><mi>S</mi></mrow><mo>)</mo></math></span> of peakons for the <em>μ</em>-version equations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"434 ","pages":"Article 113311"},"PeriodicalIF":2.4,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143821080","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

Stationary Navier–Stokes equations on the half spaces in the scaling critical framework

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-04-10 DOI: 10.1016/j.jde.2025.113298

Mikihiro Fujii

引用次数: 0

Partial boundary regularity for the Navier–Stokes equations in time-dependent domains

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-04-10 DOI: 10.1016/j.jde.2025.113299

Dominic Breit

引用次数: 0