. The purpose of this paper is to investigate the nonexistence of positive solutions of the following doubly nonlinear degenerate parabolic equations: where Ω is a Carnot-Carath´eodory metric ball in R 2 n + 1 generated by Greiner vector fields, V ∈ L 1 loc ( Ω ) , k ∈ N , m ∈ R , 1 < p < 2 n + 2 k and m + p − 2 > 0. The better lower bound p ∗ for m + p is found and the nonexistence results are proved for p ∗ 6 m + p < 3.
． 本文的目的是研究以下双非线性退化抛物方程的正解的不存在性:其中Ω是由Greiner向量场生成的r2n + 1中的Carnot-Carath ' eodory公制球，V∈l1loc (Ω)， k∈n, m∈R, 1 < p < 2n + 2k, m + p−2 > 0。找到了m + p的较好的下界p∗，并证明了p∗6 m + p < 3时的不存在性结果。
{"title":"Doubly Nonlinear Degenerate Parabolic Equations with a Singular Potential for Greiner Vector Fields","authors":"Junqiang Han","doi":"10.4208/jpde.v35.n4.1","DOIUrl":"https://doi.org/10.4208/jpde.v35.n4.1","url":null,"abstract":". The purpose of this paper is to investigate the nonexistence of positive solutions of the following doubly nonlinear degenerate parabolic equations: where Ω is a Carnot-Carath´eodory metric ball in R 2 n + 1 generated by Greiner vector fields, V ∈ L 1 loc ( Ω ) , k ∈ N , m ∈ R , 1 < p < 2 n + 2 k and m + p − 2 > 0. The better lower bound p ∗ for m + p is found and the nonexistence results are proved for p ∗ 6 m + p < 3.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":"3 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72821918","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}
. Denote v ≥ ψ , a.e. and v − θ p Ω ) o where ψ is any function in Ω ⊂ R N , N ≥ 2, with values in R ∪{± ∞ } and θ is a measurable function. This paper deals with global integrability for u ∈K ψ , θ such that with |A ( x , ξ ) |≈| ξ | p − 1 , 1 < p < N . Some global integrability results are obtained.
。表示v≥ψ， a.e.和v - θ p Ω) o，其中ψ是Ω∧R N, N≥2中的任意函数，其值在R∪{±∞}中，θ是可测函数。本文研究了u∈K ψ， θ的整体可积性，使得|A (x， ξ) |≈| ξ | p−1,1 < p < N。得到了一些全局可积性的结果。
{"title":"Global Integrability for Solutions to Obstacle Problems","authors":"Yanan Shan null, Hongya Gao","doi":"10.4208/jpde.v35.n4.2","DOIUrl":"https://doi.org/10.4208/jpde.v35.n4.2","url":null,"abstract":". Denote v ≥ ψ , a.e. and v − θ p Ω ) o where ψ is any function in Ω ⊂ R N , N ≥ 2, with values in R ∪{± ∞ } and θ is a measurable function. This paper deals with global integrability for u ∈K ψ , θ such that with |A ( x , ξ ) |≈| ξ | p − 1 , 1 < p < N . Some global integrability results are obtained.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":"4 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81596895","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":"The Obstacle Problem For Nonlinear Degenerate Elliptic Equations with Variable Exponents and L$^1$-Data","authors":"H. Khelifi","doi":"10.4208/jpde.v35.n2.1","DOIUrl":"https://doi.org/10.4208/jpde.v35.n2.1","url":null,"abstract":"","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":"101 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91218907","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 Behavior of Solutions for the Porous Media Equations with Nonlinear Norm-type Sources","authors":"Yingzhen Xue","doi":"10.4208/jpde.v35.n3.4","DOIUrl":"https://doi.org/10.4208/jpde.v35.n3.4","url":null,"abstract":"","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":"7 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91302621","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 prove the symmetry of the solution to overdetermined problem for the equation σk(D 2 u − uI) = C n in hyperbolic space. Our approach is based on establishing a RellichPohozaev type identity and using a P function. Our result generalizes the overdetermined problem for Hessian equation in Euclidean space.
{"title":"Serrin-Type Overdetermined Problem in $mathbb H^n$","authors":"Zhenghuan Gao, Xiaohan Jia, Jingquan Yan","doi":"10.4208/jpde.v36.n1.7","DOIUrl":"https://doi.org/10.4208/jpde.v36.n1.7","url":null,"abstract":"In this paper, we prove the symmetry of the solution to overdetermined problem for the equation σk(D 2 u − uI) = C n in hyperbolic space. Our approach is based on establishing a RellichPohozaev type identity and using a P function. Our result generalizes the overdetermined problem for Hessian equation in Euclidean space.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":"16 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75128768","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":"Integrated Pest Management System with Impulsive Control of Spatial Heterogeneity","authors":"H. Zhou","doi":"10.4208/jpde.v35.n1.3","DOIUrl":"https://doi.org/10.4208/jpde.v35.n1.3","url":null,"abstract":"","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":"4 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75278588","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":"Gelfand-Shilov Smoothing Effect for the Radially Symmetric Spatially Homogeneous Landau Equation under the Hard Potential γ=2","authors":"Haoguang Wang","doi":"10.4208/jpde.v35.n1.2","DOIUrl":"https://doi.org/10.4208/jpde.v35.n1.2","url":null,"abstract":"","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":"8 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81510361","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}
Shailesh A. Bhanotar & Fethi Bin Muhammad Belgacem
{"title":"Theory and Applications of Distinctive Conformable Triple Laplace and Sumudu Transforms Decomposition Methods","authors":"Shailesh A. Bhanotar & Fethi Bin Muhammad Belgacem","doi":"10.4208/jpde.v35.n1.4","DOIUrl":"https://doi.org/10.4208/jpde.v35.n1.4","url":null,"abstract":"","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":"186 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77482070","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":"Blow-up of Classical Solutions to the Isentropic Compressible Barotropic Navier-Stokes-Langevin-Korteweg Equations","authors":"Ke-Xiang Hu","doi":"10.4208/jpde.v35.n1.5","DOIUrl":"https://doi.org/10.4208/jpde.v35.n1.5","url":null,"abstract":"","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":"23 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87626460","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":"The Method of Fundamental Solution for a Radially Symmetric Heat Conduction Problem with Variable Coefficient","authors":"global RuiMa","doi":"10.4208/jpde.v34.n3.4","DOIUrl":"https://doi.org/10.4208/jpde.v34.n3.4","url":null,"abstract":"","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":"113 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81026258","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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