. We prove the existence of multiple solutions of an elliptic equation with critical Sobolev growth and critical Hardy potential on compact Riemannian manifolds.
.我们证明了紧凑黎曼流形上具有临界索波列夫增长和临界哈代势的椭圆方程多解的存在性。
{"title":"Multiple Solutions for an Elliptic Equation with Hardy Potential and Critical Nonlinearity on Compact Riemannian Manifolds","authors":"Maliki Youssef null, Terki Fatima Zohra","doi":"10.4208/jpde.v37.n1.1","DOIUrl":"https://doi.org/10.4208/jpde.v37.n1.1","url":null,"abstract":". We prove the existence of multiple solutions of an elliptic equation with critical Sobolev growth and critical Hardy potential on compact Riemannian manifolds.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141229593","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. The viability of the conformable stochastic differential equations is studied. Some necessary and sufficient conditions in terms of the distance function to K are given. In addition, when the boundary of K is sufficiently smooth, our necessary and sufficient conditions can reduce to two relations just on the boundary of K . Lastly, an example is given to illustrate our main results.
.研究了符合随机微分方程的可行性。给出了一些与 K 的距离函数相关的必要条件和充分条件。此外，当 K 的边界足够光滑时，我们的必要条件和充分条件可以简化为 K 边界上的两个关系。最后，举例说明我们的主要结果。
{"title":"On the Viability of Solutions to Conformable Stochastic Differential Equations","authors":"Liping XU null, Zhi Li","doi":"10.4208/jpde.v37.n1.3","DOIUrl":"https://doi.org/10.4208/jpde.v37.n1.3","url":null,"abstract":". The viability of the conformable stochastic differential equations is studied. Some necessary and sufficient conditions in terms of the distance function to K are given. In addition, when the boundary of K is sufficiently smooth, our necessary and sufficient conditions can reduce to two relations just on the boundary of K . Lastly, an example is given to illustrate our main results.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141235664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. This paper is concerned with the pullback dynamics and robustness for the 2D incompressible Navier-Stokes equations with delay on the convective term in bounded domain. Under appropriate assumption on the delay term, we establish the existence of pullback attractors for the fluid flow model, which is dependent on the past state. Inspired by the idea in Zelati and Gal’s paper (JMFM, 2015), the robustness of pullback attractors has been proved via upper semi-continuity in last section
.本文关注有界域中对流项有延迟的二维不可压缩纳维-斯托克斯方程的回拉动力学和鲁棒性。在延迟项的适当假设下，我们建立了流体流动模型的回拉吸引子的存在性，它取决于过去的状态。受 Zelati 和 Gal 论文（JMFM，2015 年）的启发，上一节通过上半连续性证明了回拉吸引子的稳健性
{"title":"Robustness of Pullback Attractors for 2D Incompressible Navier-Stokes Equations with Delay","authors":"Keqin SU null, Xinguang Yang","doi":"10.4208/jpde.v37.n1.2","DOIUrl":"https://doi.org/10.4208/jpde.v37.n1.2","url":null,"abstract":". This paper is concerned with the pullback dynamics and robustness for the 2D incompressible Navier-Stokes equations with delay on the convective term in bounded domain. Under appropriate assumption on the delay term, we establish the existence of pullback attractors for the fluid flow model, which is dependent on the past state. Inspired by the idea in Zelati and Gal’s paper (JMFM, 2015), the robustness of pullback attractors has been proved via upper semi-continuity in last section","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141233125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. The biwave maps are a class of fourth order hyperbolic equations. In this paper, we are interested in the solution formulas of the linear homogeneous biwave equations. Based on the solution formulas and the weighted energy estimate, we can obtain the L ∞ ( R n ) − W N ,1 ( R n ) and L ∞ ( R n ) − W N ,2 ( R n ) estimates, respectively. By our results, we find that the biwave maps enjoy some different properties compared with the standard wave equations
.双波映射是一类四阶双曲方程。本文主要研究线性均质双波方程的求解公式。根据求解公式和加权能量估计，我们可以分别得到 L ∞ ( R n ) - W N ,1 ( R n ) 和 L ∞ ( R n ) - W N ,2 ( R n ) 估计值。根据我们的结果，我们发现双波图与标准波方程相比具有一些不同的性质
{"title":"On Linear Homogeneous Biwave Equations","authors":"Yaqian Bai","doi":"10.4208/jpde.v37.n1.4","DOIUrl":"https://doi.org/10.4208/jpde.v37.n1.4","url":null,"abstract":". The biwave maps are a class of fourth order hyperbolic equations. In this paper, we are interested in the solution formulas of the linear homogeneous biwave equations. Based on the solution formulas and the weighted energy estimate, we can obtain the L ∞ ( R n ) − W N ,1 ( R n ) and L ∞ ( R n ) − W N ,2 ( R n ) estimates, respectively. By our results, we find that the biwave maps enjoy some different properties compared with the standard wave equations","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141232934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. In this paper, we study the quenching phenomenon of solutions for parabolic equations with singular absorption under the mixed boundary conditions on graphs. Firstly, we prove the local existence of solutions via Schauder fixed point theorem. Then, under certain conditions we obtain the estimates of quenching time and quenching rate. Finally, numerical experiments are shown to explain the theoretical results.
{"title":"Quenching Phenomenon of Solutions for Parabolic Equations with Singular Absorption on Graphs","authors":"Liping Zhu, Yaxin Zhou null, Lin Huang","doi":"10.4208/jpde.v37.n1.6","DOIUrl":"https://doi.org/10.4208/jpde.v37.n1.6","url":null,"abstract":". In this paper, we study the quenching phenomenon of solutions for parabolic equations with singular absorption under the mixed boundary conditions on graphs. Firstly, we prove the local existence of solutions via Schauder fixed point theorem. Then, under certain conditions we obtain the estimates of quenching time and quenching rate. Finally, numerical experiments are shown to explain the theoretical results.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141230501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
EL Ouaarabi Mohamed, Allalou Chakir null, Melliani Said
{"title":"Existence of Weak Solution for $p(x)$-Kirchhoff Type Problem Involving the $p(x)$-Laplacian-like Operator by Topological Degree","authors":"EL Ouaarabi Mohamed, Allalou Chakir null, Melliani Said","doi":"10.4208/jpde.v36.n2.5","DOIUrl":"https://doi.org/10.4208/jpde.v36.n2.5","url":null,"abstract":"","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81017488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Achievements and Contributions in the Field of Partial Differential Equations: Special Issue Dedicated to Academician Zhou Yulin’s Centenary Birthday","authors":"G. Boling","doi":"10.4208/jpde.v36.n2.1","DOIUrl":"https://doi.org/10.4208/jpde.v36.n2.1","url":null,"abstract":"","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87537047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An Elliptic Nonlinear System of Two Functions with Application","authors":"Kang Joon Hyuk null, Roberts Timothy","doi":"10.4208/jpde.v36.n2.2","DOIUrl":"https://doi.org/10.4208/jpde.v36.n2.2","url":null,"abstract":"","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73635522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. We consider a class of free boundary problems with Neumann boundary conditions. We would like to give certain results with regularity of solutions (mainly the local interior and boundary Lipschitz continuity). We will also show an explicit form of solution under well-specified conditions.
{"title":"Lipschitz Continuity and Explicit Form of Solution in a Class of Free Boundary Problem with Neumann Boundary Condition","authors":"SAADI Abderachid","doi":"10.4208/jpde.v36.n4.1","DOIUrl":"https://doi.org/10.4208/jpde.v36.n4.1","url":null,"abstract":". We consider a class of free boundary problems with Neumann boundary conditions. We would like to give certain results with regularity of solutions (mainly the local interior and boundary Lipschitz continuity). We will also show an explicit form of solution under well-specified conditions.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135194306","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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