{"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":"23 1","pages":""},"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}
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":"100 1","pages":""},"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":"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":"245 1","pages":""},"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":"5 1","pages":"0"},"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}
{"title":"A New Regularization Method for a Parameter Identification Problem in a Non-linear Partial Differential Equation","authors":"N. M. T. null, Roy Samprita Das","doi":"10.4208/jpde.v36.n2.3","DOIUrl":"https://doi.org/10.4208/jpde.v36.n2.3","url":null,"abstract":"","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":"35 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88304820","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":"Blowup of the Solutions for a Reaction-AdvectionDiffusion Equation with Free Boundaries","authors":"Jian YANG","doi":"10.4208/jpde.v36.n4.5","DOIUrl":"https://doi.org/10.4208/jpde.v36.n4.5","url":null,"abstract":"","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":"126 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135194308","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 well-posedness and blow-up solutions for the fractional Schr¨odinger equation with a Hartree-type nonlinearity together with a power-type subcritical or critical perturbations. For nonradial initial data or radial initial data, we prove the local well-posedness for the defocusing and the focusing cases with sub-critical or critical nonlinearity. We obtain the global well-posedness for the defocusing case, and for the focusing mass-subcritical case or mass-critical case with initial data small enough. We also investigate blow-up solutions for the focusing mass-critical problem.
{"title":"Well-Posedness and Blow-Up for the Fractional Schrödinger- Choquard Equation","authors":"Lu Tao, Yajuan Zhao null, Yongsheng Li","doi":"10.4208/jpde.v36.n1.6","DOIUrl":"https://doi.org/10.4208/jpde.v36.n1.6","url":null,"abstract":". In this paper, we study the well-posedness and blow-up solutions for the fractional Schr¨odinger equation with a Hartree-type nonlinearity together with a power-type subcritical or critical perturbations. For nonradial initial data or radial initial data, we prove the local well-posedness for the defocusing and the focusing cases with sub-critical or critical nonlinearity. We obtain the global well-posedness for the defocusing case, and for the focusing mass-subcritical case or mass-critical case with initial data small enough. We also investigate blow-up solutions for the focusing mass-critical problem.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":"101 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84727062","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":"Asymptotic Stability for a Quasilinear Viscoelastic Equation with Nonlinear Damping and Memory","authors":"Xiaoming PENG null, Yadong SHANG","doi":"10.4208/jpde.v36.n4.2","DOIUrl":"https://doi.org/10.4208/jpde.v36.n4.2","url":null,"abstract":"","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135194307","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}
. Regularity criteria in terms of bounds for the pressure are derived for the 3D MHD equations in a bounded domain with slip boundary conditions. A list of three regularity criteria is shown.
． 导出了具有滑移边界条件的有界区域内三维MHD方程的压力规则准则。显示了三个规则标准的列表。
{"title":"Regularity Criteria of the Magnetohydrodynamic Equations in a Bounded Domain","authors":"Jishan Fan null, Q. Ju","doi":"10.4208/jpde.v36.n3.5","DOIUrl":"https://doi.org/10.4208/jpde.v36.n3.5","url":null,"abstract":". Regularity criteria in terms of bounds for the pressure are derived for the 3D MHD equations in a bounded domain with slip boundary conditions. A list of three regularity criteria is shown.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":"73 8 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87779136","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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