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Stochastic porous media equation with Robin boundary conditions, gravity-driven infiltration and multiplicative noise
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-04-25 DOI: 10.1016/j.jde.2025.113363
Ioana Ciotir , Dan Goreac , Juan Li , Antoine Tonnoir
{"title":"Stochastic porous media equation with Robin boundary conditions, gravity-driven infiltration and multiplicative noise","authors":"Ioana Ciotir ,&nbsp;Dan Goreac ,&nbsp;Juan Li ,&nbsp;Antoine Tonnoir","doi":"10.1016/j.jde.2025.113363","DOIUrl":"10.1016/j.jde.2025.113363","url":null,"abstract":"<div><div>We aim at studying a novel mathematical model associated to a physical phenomenon of infiltration in an homogeneous porous medium. The particularities of our system are connected to the presence of a gravitational acceleration term proportional to the level of saturation, and of a Brownian multiplicative perturbation. Furthermore, the boundary conditions intervene in a Robin manner with the distinction of the behavior along the inflow and outflow respectively. We provide qualitative results of well-posedness, the investigation being conducted through a functional approach.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"438 ","pages":"Article 113363"},"PeriodicalIF":2.4,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870204","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
Asymptotic behavior of solutions to the Cauchy problem for 1D p-system with spatiotemporal damping: Case 1. v+ = v−
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-04-24 DOI: 10.1016/j.jde.2025.113347
Yang Cai , Changchun Liu , Ming Mei , Zejia Wang
{"title":"Asymptotic behavior of solutions to the Cauchy problem for 1D p-system with spatiotemporal damping: Case 1. v+ = v−","authors":"Yang Cai ,&nbsp;Changchun Liu ,&nbsp;Ming Mei ,&nbsp;Zejia Wang","doi":"10.1016/j.jde.2025.113347","DOIUrl":"10.1016/j.jde.2025.113347","url":null,"abstract":"<div><div>This paper investigates the Cauchy problem for the <em>p</em>-system with spatiotemporal damping, modeling one-dimensional compressible flow through porous media in Lagrangian coordinates. We focus on the large-time asymptotic behavior of the system's solutions when the state constants for the specific volume are the same: <span><math><msub><mrow><mi>v</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>=</mo><msub><mrow><mi>v</mi></mrow><mrow><mo>−</mo></mrow></msub></math></span>, but the state constants for the velocity are different: <span><math><msub><mrow><mi>u</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>≠</mo><msub><mrow><mi>u</mi></mrow><mrow><mo>−</mo></mrow></msub></math></span>. We show the convergence of the solutions to their diffusion waves with the different algebraic time decay rates according to different exponent of time-damping: <span><math><mn>0</mn><mo>≤</mo><mi>λ</mi><mo>&lt;</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>5</mn></mrow></mfrac></math></span>, <span><math><mi>λ</mi><mo>=</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>5</mn></mrow></mfrac></math></span> and <span><math><mfrac><mrow><mn>3</mn></mrow><mrow><mn>5</mn></mrow></mfrac><mo>&lt;</mo><mi>λ</mi><mo>&lt;</mo><mn>1</mn></math></span>, respectively. Our analysis employs an energy method to establish a series of a priori estimates, offering new insights and theoretical support for understanding the long-time dynamics of compressible flows in porous media with spatially heterogeneous damping.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"436 ","pages":"Article 113347"},"PeriodicalIF":2.4,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143865114","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
Positive nonradial solutions of an elliptic equation with critical advection term
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-04-24 DOI: 10.1016/j.jde.2025.113346
A. Aghajani , C. Cowan
{"title":"Positive nonradial solutions of an elliptic equation with critical advection term","authors":"A. Aghajani ,&nbsp;C. Cowan","doi":"10.1016/j.jde.2025.113346","DOIUrl":"10.1016/j.jde.2025.113346","url":null,"abstract":"<div><div>Consider the problem<span><span><span>(1)</span><span><math><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>−</mo><mfrac><mrow><mi>β</mi><mi>x</mi><mo>⋅</mo><mi>∇</mi><mi>u</mi></mrow><mrow><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo>+</mo><mi>u</mi><mo>=</mo><msup><mrow><mi>u</mi></mrow><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow></msup><mtext> in </mtext><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>,</mo></math></span></span></span> where <span><math><mi>p</mi><mo>&gt;</mo><mn>2</mn></math></span>, <span><math><mi>β</mi><mo>&gt;</mo><mn>0</mn></math></span> and <span><math><mi>N</mi><mo>=</mo><mn>2</mn><mi>n</mi><mo>≥</mo><mn>4</mn></math></span> an even integer. In this work we are interested in finding positive classical nonradial solutions of <span><span>(1)</span></span>. We also consider the problem on the unit ball. We demonstrate the existence of a positive bounded solution for the range <span><math><mn>2</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>β</mi></mrow></msub><mo>:</mo><mo>=</mo><mfrac><mrow><mi>N</mi><mo>+</mo><mn>2</mn><mi>β</mi></mrow><mrow><mi>N</mi><mo>−</mo><mn>2</mn><mo>+</mo><mi>β</mi></mrow></mfrac></math></span>, and show that nonradial solutions exist for a specific range of <em>p</em>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"436 ","pages":"Article 113346"},"PeriodicalIF":2.4,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143865115","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
A hyperbolic relaxation approximation of the incompressible Navier-Stokes equations with artificial compressibility
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-04-24 DOI: 10.1016/j.jde.2025.113339
Qian Huang , Christian Rohde , Wen-An Yong , Ruixi Zhang
{"title":"A hyperbolic relaxation approximation of the incompressible Navier-Stokes equations with artificial compressibility","authors":"Qian Huang ,&nbsp;Christian Rohde ,&nbsp;Wen-An Yong ,&nbsp;Ruixi Zhang","doi":"10.1016/j.jde.2025.113339","DOIUrl":"10.1016/j.jde.2025.113339","url":null,"abstract":"<div><div>We introduce a new hyperbolic approximation to the incompressible Navier-Stokes equations by incorporating a first-order relaxation and using the artificial compressibility method. With two relaxation parameters in the model, we rigorously prove the asymptotic limit of the system towards the incompressible Navier-Stokes equations as both parameters tend to zero. Notably, the convergence of the approximate pressure variable is achieved by the help of a linear ‘auxiliary’ system and energy-type error estimates of the differences between the two-parameter model and the Navier-Stokes equations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"438 ","pages":"Article 113339"},"PeriodicalIF":2.4,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870202","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 Calderón-Zygmund theory for fractional Laplacian type equations
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-04-23 DOI: 10.1016/j.jde.2025.113319
Sun-Sig Byun , Kyeongbae Kim , Deepak Kumar
{"title":"Global Calderón-Zygmund theory for fractional Laplacian type equations","authors":"Sun-Sig Byun ,&nbsp;Kyeongbae Kim ,&nbsp;Deepak Kumar","doi":"10.1016/j.jde.2025.113319","DOIUrl":"10.1016/j.jde.2025.113319","url":null,"abstract":"<div><div>We establish several fine boundary regularity results of weak solutions to non-homogeneous <em>s</em>-fractional Laplacian type equations. In particular, we prove sharp Calderón-Zygmund type estimates of <span><math><mi>u</mi><mo>/</mo><msup><mrow><mi>d</mi></mrow><mrow><mi>s</mi></mrow></msup></math></span> depending on the regularity assumptions on the associated kernel coefficient including VMO, Dini continuity or the Hölder continuity, where <em>u</em> is a weak solution to such a nonlocal problem and <em>d</em> is the distance to the boundary function of a given domain. Our analysis is based on point-wise behaviors of maximal functions of <span><math><mi>u</mi><mo>/</mo><msup><mrow><mi>d</mi></mrow><mrow><mi>s</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"436 ","pages":"Article 113319"},"PeriodicalIF":2.4,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143860718","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 bifurcation of homoclinic solutions 同轴解的全局分岔
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-04-23 DOI: 10.1016/j.jde.2025.113334
Iacopo P. Longo , Christian Pötzsche , Robert Skiba
{"title":"Global bifurcation of homoclinic solutions","authors":"Iacopo P. Longo ,&nbsp;Christian Pötzsche ,&nbsp;Robert Skiba","doi":"10.1016/j.jde.2025.113334","DOIUrl":"10.1016/j.jde.2025.113334","url":null,"abstract":"<div><div>In the analysis of parameterized nonautonomous evolutionary equations, bounded entire solutions are natural candidates for bifurcating objects. Appropriate explicit and sufficient conditions for such branchings, however, require to combine contemporary functional analytical methods from the abstract bifurcation theory for Fredholm operators with tools originating in dynamical systems.</div><div>This paper establishes alternatives classifying the shape of global bifurcating branches of bounded entire solutions to Carathéodory differential equations. Our approach is based on the parity associated to a path of index 0 Fredholm operators, the global Evans function as a recent tool in nonautonomous bifurcation theory and suitable topologies on spaces of Carathéodory functions.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"437 ","pages":"Article 113334"},"PeriodicalIF":2.4,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143858929","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 a nonlocal competition model in moving environment: The effects of impulsive interventions 移动环境中的非局部竞争模型：冲动干预的影响
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-04-22 DOI: 10.1016/j.jde.2025.113337
Yue Meng , Zhigui Lin , Jiazheng Zhou
{"title":"On a nonlocal competition model in moving environment: The effects of impulsive interventions","authors":"Yue Meng ,&nbsp;Zhigui Lin ,&nbsp;Jiazheng Zhou","doi":"10.1016/j.jde.2025.113337","DOIUrl":"10.1016/j.jde.2025.113337","url":null,"abstract":"<div><div>Considering the long distance dispersal and human interventions on species, a free boundary problem for the competition model with nonlocal diffusion and periodic pulses is investigated. The principal eigenvalue of time-dependent eigenvalue problem, which depends on the length of habitat and impulsive intensity, is defined and analyzed. This index can be used to characterize the dynamics for three different competition cases: (<em>a</em>) invasive species is the inferior, (<em>b</em>) invasive species is the superior and (<em>c</em>) the competition is weak. Our results not only extend the existing ones for the cases without pulses, but also reveal that the introduction of human interventions makes the long time behaviors of competitors complex and diverse, and can alter the competition outcomes. In addition, whether the invasive species can eventually survive in the new environment depends not only on the imposed pulse, but also on the initial region and its own expanding capability in case (<em>b</em>).</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"434 ","pages":"Article 113337"},"PeriodicalIF":2.4,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143855102","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 bifurcation diagrams for coercive third-degree polynomial ordinary differential equations with recurrent nonautonomous coefficients
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-04-22 DOI: 10.1016/j.jde.2025.113315
Cinzia Elia , Roberta Fabbri , Carmen Núñez
{"title":"Global bifurcation diagrams for coercive third-degree polynomial ordinary differential equations with recurrent nonautonomous coefficients","authors":"Cinzia Elia ,&nbsp;Roberta Fabbri ,&nbsp;Carmen Núñez","doi":"10.1016/j.jde.2025.113315","DOIUrl":"10.1016/j.jde.2025.113315","url":null,"abstract":"<div><div>Nonautonomous bifurcation theory is a growing branch of mathematics, for the insight it provides into radical changes in the global dynamics of realistic models for many real-world phenomena, i.e., into the occurrence of critical transitions. This paper describes several global bifurcation diagrams for nonautonomous first order scalar ordinary differential equations generated by coercive third degree polynomials in the state variable. The conclusions are applied to a population dynamics model subject to an Allee effect that is weak in the absence of migration and becomes strong under a migratory phenomenon whose sense and intensity depend on a threshold in the number of individuals in the population.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"435 ","pages":"Article 113315"},"PeriodicalIF":2.4,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143855105","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
Dynamics for a nonlocal logistic equation with a sedentary compartment and free boundary
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-04-22 DOI: 10.1016/j.jde.2025.113336
Xueping Li , Lei Li , Mingxin Wang
{"title":"Dynamics for a nonlocal logistic equation with a sedentary compartment and free boundary","authors":"Xueping Li ,&nbsp;Lei Li ,&nbsp;Mingxin Wang","doi":"10.1016/j.jde.2025.113336","DOIUrl":"10.1016/j.jde.2025.113336","url":null,"abstract":"<div><div>This paper investigates a nonlocal logistic equation with a sedentary compartment and free boundary, where population dispersal is modeled using nonlocal diffusion. We first show a spreading-vanishing dichotomy holds. Then by varying the intrinsic rate <em>r</em> of reproduction and diffusion coefficient <em>d</em> respectively, we give detailed criteria for spreading and vanishing, which reveals that the larger <em>r</em> is (or the smaller <em>d</em> is), the more likely spreading is to happen. When spreading occurs, we prove that if and only if a threshold condition is satisfied by kernel function <em>J</em>, there exists a unique finite spreading speed of free boundary which is proved to be the asymptotic spreading speed of density functions <em>u</em> and <em>v</em>. Moreover, we also show that the level sets of <em>u</em> and <em>v</em> have the same spreading speed with free boundaries <span><math><mi>g</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span> and <span><math><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"435 ","pages":"Article 113336"},"PeriodicalIF":2.4,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143855103","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 local strong solutions to the Cauchy problem of 3D isentropic compressible Navier-Stokes equations with degenerate viscosities and far field vacuum
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-04-22 DOI: 10.1016/j.jde.2025.113338
Jiaxu Li , Lixin Li
{"title":"On local strong solutions to the Cauchy problem of 3D isentropic compressible Navier-Stokes equations with degenerate viscosities and far field vacuum","authors":"Jiaxu Li ,&nbsp;Lixin Li","doi":"10.1016/j.jde.2025.113338","DOIUrl":"10.1016/j.jde.2025.113338","url":null,"abstract":"<div><div>This paper concerns the Cauchy problem of the isentropic compressible Navier-Stokes equations with degenerate viscosities and far-field vacuum. When the shear and the bulk viscosity are power functions of the density (<span><math><msup><mrow><mi>ρ</mi></mrow><mrow><mi>δ</mi></mrow></msup></math></span> with <span><math><mn>0</mn><mo>&lt;</mo><mi>δ</mi><mo>&lt;</mo><mn>1</mn></math></span>), it is proved that the three-dimensional Cauchy problem of the compressible Navier-Stokes equations admits a unique strong solution provided the initial density decays as <span><math><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mo>−</mo><mi>α</mi></mrow></msup><mo>(</mo><msup><mrow><mo>(</mo><mn>2</mn><mi>γ</mi><mo>−</mo><mn>1</mn><mo>−</mo><mi>δ</mi><mo>)</mo></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>&lt;</mo><mi>α</mi><mo>&lt;</mo><mn>2</mn><mo>(</mo><mn>3</mn><mo>−</mo><mn>2</mn><mi>ε</mi><mo>)</mo><mo>/</mo><mo>(</mo><mn>1</mn><mo>−</mo><mi>δ</mi><mo>)</mo><mo>(</mo><mn>3</mn><mo>−</mo><mi>ε</mi><mo>)</mo><mo>)</mo></math></span> at infinity with <span><math><mi>γ</mi><mo>&gt;</mo><mn>1</mn></math></span> and <span><math><mi>ε</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>. Notably, the choice of <em>δ</em> can be made independently of <em>γ</em>, broadening the range of permissible <em>δ</em> values compared to previous studies. Consequently, these findings have broader applicability to a diverse array of physical models, including those involving Maxwellian molecules.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"435 ","pages":"Article 113338"},"PeriodicalIF":2.4,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143855104","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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