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Blowup Behavior of Solutions to an $omega$-diffusion Equation on the Graph $ ω $-扩散方程解在图上的爆破行为
IF 0.3 4区 数学
Journal of Partial Differential Equations Pub Date : 2022-06-01 DOI: 10.4208/jpde.v35.n2.3
Liping Zhu null, Lin Huang
{"title":"Blowup Behavior of Solutions to an $omega$-diffusion Equation on the Graph","authors":"Liping Zhu null, Lin Huang","doi":"10.4208/jpde.v35.n2.3","DOIUrl":"https://doi.org/10.4208/jpde.v35.n2.3","url":null,"abstract":"","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":"176 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76227262","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}
引用次数: 0
Boundedness for a Class of Operators on Weighted Morrey Space with RD-measure 带rd测度的加权Morrey空间上一类算子的有界性
IF 0.3 4区 数学
Journal of Partial Differential Equations Pub Date : 2022-06-01 DOI: 10.4208/jpde.v35.n4.7
Xiaona Cui, Yongjin Lu null, Mengmeng Li
{"title":"Boundedness for a Class of Operators on Weighted Morrey Space with RD-measure","authors":"Xiaona Cui, Yongjin Lu null, Mengmeng Li","doi":"10.4208/jpde.v35.n4.7","DOIUrl":"https://doi.org/10.4208/jpde.v35.n4.7","url":null,"abstract":". In this paper, we study a class of sublinear operators and their commutators with a weighted BMO function. We first give the definition of a weighted Morrey space L p , κ µ , ω ( X ) where X is an RD-measure and ω is the weight function. The weighted Morrey spaces arise from studying the local behavior of solutions to certain partial differential equations. We will show that the aforementioned class of operators and their communtators with a weighted BMO function are bounded in the weighted Morrey space L p , κ µ , ω ( X ) provided that the weight function ω belongs to the A p ( µ ) -class and satisfies the reverse H¨older’s condition.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":"56 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74043010","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}
引用次数: 0
Exact Boundary Controllability of Fifth-order KdV Equation Posed on the Periodic Domain 周期域上五阶KdV方程的精确边界可控性
IF 0.3 4区 数学
Journal of Partial Differential Equations Pub Date : 2022-06-01 DOI: 10.4208/jpde.v35.n2.4
Shuning Yang null, Xiangqing Zhao
{"title":"Exact Boundary Controllability of Fifth-order KdV Equation Posed on the Periodic Domain","authors":"Shuning Yang null, Xiangqing Zhao","doi":"10.4208/jpde.v35.n2.4","DOIUrl":"https://doi.org/10.4208/jpde.v35.n2.4","url":null,"abstract":"","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":"30 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82992504","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}
引用次数: 0
Positive Ground State Solutions for a Critical Nonlocal Problem in Dimension Three 三维临界非局部问题的正基态解
IF 0.3 4区 数学
Journal of Partial Differential Equations Pub Date : 2022-06-01 DOI: 10.4208/jpde.v35.n4.6
X. Qian
{"title":"Positive Ground State Solutions for a Critical Nonlocal Problem in Dimension Three","authors":"X. Qian","doi":"10.4208/jpde.v35.n4.6","DOIUrl":"https://doi.org/10.4208/jpde.v35.n4.6","url":null,"abstract":". In this paper, we are interested in the following nonlocal problem with critical exponent where a , b are positive constants, 2 < p < 6, Ω is a smooth bounded domain in R 3 and λ > 0 is a parameter. By variational methods, we prove that problem has a positive ground state solution u b for λ > 0 sufficiently large. Moreover, we take b as a parameter and study the asymptotic behavior of u b when b ց 0.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":"47 2 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83189563","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}
引用次数: 0
On Local Well posedness of the Schrödinger-Boussinesq Systems 关于Schrödinger-Boussinesq系统的局部适定性
IF 0.3 4区 数学
Journal of Partial Differential Equations Pub Date : 2022-06-01 DOI: 10.4208/jpde.v35.n4.5
N. Null
{"title":"On Local Well posedness of the Schrödinger-Boussinesq Systems","authors":"N. Null","doi":"10.4208/jpde.v35.n4.5","DOIUrl":"https://doi.org/10.4208/jpde.v35.n4.5","url":null,"abstract":"","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":" 30","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72499577","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}
引用次数: 0
A Singular Moser-Trudinger Inequality on Metric Measure Space 度量测度空间上的一个奇异Moser-Trudinger不等式
IF 0.3 4区 数学
Journal of Partial Differential Equations Pub Date : 2022-06-01 DOI: 10.4208/jpde.v35.n4.3
Yaoting Gui
{"title":"A Singular Moser-Trudinger Inequality on Metric Measure Space","authors":"Yaoting Gui","doi":"10.4208/jpde.v35.n4.3","DOIUrl":"https://doi.org/10.4208/jpde.v35.n4.3","url":null,"abstract":". Let ( X , d , µ ) be a metric space with a Borel-measure µ , suppose µ satisfies the Ahlfors-regular condition, i.e. where b 1 , b 2 are two positive constants and s is the volume growth exponent. In this paper, we mainly study two things, one is to consider the best constant of the Moser-Trudinger inequality on such metric space under the condition that s is not less than 2. The other is to study the generalized Moser-Trudinger inequality with a singular weight.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":"154 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86043312","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}
引用次数: 0
Infinitely Many Solutions for the Fractional Nonlinear Schrödinger Equations of a New Type 一类新型分数阶非线性Schrödinger方程的无穷多解
IF 0.3 4区 数学
Journal of Partial Differential Equations Pub Date : 2022-06-01 DOI: 10.4208/jpde.v35.n3.5
Qing Guo null, Lixiu Duan
{"title":"Infinitely Many Solutions for the Fractional Nonlinear Schrödinger Equations of a New Type","authors":"Qing Guo null, Lixiu Duan","doi":"10.4208/jpde.v35.n3.5","DOIUrl":"https://doi.org/10.4208/jpde.v35.n3.5","url":null,"abstract":". This paper, we study the multiplicity of solutions for the fractional Schr¨odinger equation with s ∈ ( 0,1 ) , N ≥ 3, p ∈ ( 1, 2 N N − 2 s − 1 ) and lim | y |→ + ∞ V ( y ) > 0. By assuming suitable decay property of the radial potential V ( y ) = V ( | y | ) , we construct another type of solutions concentrating at infinite vertices of two similar equilateral polygonal with infinitely large length of sides. Hence, besides the length of each polygonal, we must consider one more parameter, that is the height of the podetium, simultaneously. Another difficulty lies in the non-local property of the operator ( − ∆ ) s and the algebraic decay involving the approximation solutions make the estimates become more subtle.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":"56 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83973831","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}
引用次数: 0
Mean Field Equations for the Equilibrium Turbulence and Toda Systems on Connected Finite Graphs 有限连通图上平衡湍流和Toda系统的平均场方程
IF 0.3 4区 数学
Journal of Partial Differential Equations Pub Date : 2022-06-01 DOI: 10.4208/jpde.v35.n3.1
Xiao-Dan Zhu
{"title":"Mean Field Equations for the Equilibrium Turbulence and Toda Systems on Connected Finite Graphs","authors":"Xiao-Dan Zhu","doi":"10.4208/jpde.v35.n3.1","DOIUrl":"https://doi.org/10.4208/jpde.v35.n3.1","url":null,"abstract":". In this paper, we study existence of solutions of mean field equations for the equilibrium turbulence and Toda systems on connected finite graphs. Our method is based on calculus of variations, which was built on connected finite graphs by Grigor’yan, Lin and Yang.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":"28 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74446690","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}
引用次数: 5
Global Well-Posedness of Solutions to 2D Prandtl-Hartmann Equations in Analytic Framework 解析框架下二维Prandtl-Hartmann方程解的全局适定性
IF 0.3 4区 数学
Journal of Partial Differential Equations Pub Date : 2022-06-01 DOI: 10.4208/jpde.v35.n3.7
Xiaolei Dong null, Yuming Qin
{"title":"Global Well-Posedness of Solutions to 2D Prandtl-Hartmann Equations in Analytic Framework","authors":"Xiaolei Dong null, Yuming Qin","doi":"10.4208/jpde.v35.n3.7","DOIUrl":"https://doi.org/10.4208/jpde.v35.n3.7","url":null,"abstract":". In this paper, we consider the two-dimensional (2D) Prandtl-Hartmann equations on the half plane and prove the global existence and uniqueness of solutions to 2D Prandtl-Hartmann equations by using the classical energy methods in analytic framework. We prove that the lifespan of the solutions to 2D Prandtl-Hartmann equations can be extended up to T ε (see Theorem 2.1) when the strength of the perturbation is of the order of ε . The difficulty of solving the Prandtl-Hartmann equations in the analytic framework is the loss of x -derivative in the term v ∂ y u . To overcome this difficulty, we introduce the Gaussian weighted Poincar´ e inequality (see Lemma 2.3). Com-pared to the existence and uniqueness of solutions to the classical Prandtl equations where the monotonicity condition of the tangential velocity plays a key role, which is not needed for the 2D Prandtl-Hartmann equations in analytic framework. Besides, the existence and uniqueness of solutions to the 2D MHD boundary layer where the initial tangential magnetic field has a lower bound plays an important role, which is not needed for the 2D Prandtl-Hartmann equations in analytic framework, either.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":"16 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74810291","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}
引用次数: 2
Global Well-Posedness for the 3D Tropical Climate Model without Thermal Diffusion 无热扩散的三维热带气候模式的全球适定性
IF 0.3 4区 数学
Journal of Partial Differential Equations Pub Date : 2022-06-01 DOI: 10.4208/jpde.v35.n4.4
Yanghai Yu, Jinlu Li null, Xiuwei Yin
{"title":"Global Well-Posedness for the 3D Tropical Climate Model without Thermal Diffusion","authors":"Yanghai Yu, Jinlu Li null, Xiuwei Yin","doi":"10.4208/jpde.v35.n4.4","DOIUrl":"https://doi.org/10.4208/jpde.v35.n4.4","url":null,"abstract":". In this paper, we consider the Cauchy problem of 3D tropical climate model with zero thermal diffusion. Firstly, we establish the global regularity for this system with fractional diffusion α = β = 5/4. Secondly, by adding only a damp term, we obtain the global well-posedness for small initial data.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89539675","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}
引用次数: 0
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