Rui Lu, Chunxiao Guo, Xin-Guang Yang null, P. Zhang
{"title":"Dynamics for Three Dimensional Generalized Navier- Stokes Equations with Delay","authors":"Rui Lu, Chunxiao Guo, Xin-Guang Yang null, P. Zhang","doi":"10.4208/jpde.v35.n2.2","DOIUrl":"https://doi.org/10.4208/jpde.v35.n2.2","url":null,"abstract":"","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75252164","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 have discussed solution and stability analysis of ordinary and partial differential equation with boundary value problem. We investigated pe-riodic stability in Eulers scheme and also discussed PDEs by finite difference scheme. Numerical example has been discussed finding nature of stability. All given result more accurate other than existing methods.
{"title":"Study of Stability Criteria of Numerical Solution of Ordinary and Partial Differential Equations Using Euler’s and Finite Difference Scheme","authors":"Najmuddin Ahmad null, Shiv Charan","doi":"10.4208/jpde.v35.n3.6","DOIUrl":"https://doi.org/10.4208/jpde.v35.n3.6","url":null,"abstract":". In this paper we have discussed solution and stability analysis of ordinary and partial differential equation with boundary value problem. We investigated pe-riodic stability in Eulers scheme and also discussed PDEs by finite difference scheme. Numerical example has been discussed finding nature of stability. All given result more accurate other than existing methods.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81716531","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 investigate the initial value problem for the two-dimensional magneto-micropolar fluid equations with partial viscosity. We prove that global existence of smooth large solutions by the energy method. Furthermore, with aid of the Fourier splitting methods, optimal time-decay rates of global smooth large solutions are also established.
{"title":"Global Existence and Time-decay Rates of Solutions to 2D Magneto-micropolar Fluid Equations with Partial Viscosity","authors":"Yuzhu Wang null, Yuzhu Wang","doi":"10.4208/jpde.v35.n2.5","DOIUrl":"https://doi.org/10.4208/jpde.v35.n2.5","url":null,"abstract":". In this paper, we investigate the initial value problem for the two-dimensional magneto-micropolar fluid equations with partial viscosity. We prove that global existence of smooth large solutions by the energy method. Furthermore, with aid of the Fourier splitting methods, optimal time-decay rates of global smooth large solutions are also established.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83139525","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 obtained the extremal function for a weighted singular Trudinger-Moser inequality by blow-up analysis in the Euclidean space R 2 . This ex-tends recent results of Hou (J. Inequal. Appl., 2018) and similar result was proved by Zhu (Sci. China Math., 2021).
{"title":"A Weighted Singular Trudinger-Moser Inequality","authors":"YU Peng","doi":"10.4208/jpde.v35.n3.2","DOIUrl":"https://doi.org/10.4208/jpde.v35.n3.2","url":null,"abstract":". In this paper, we obtained the extremal function for a weighted singular Trudinger-Moser inequality by blow-up analysis in the Euclidean space R 2 . This ex-tends recent results of Hou (J. Inequal. Appl., 2018) and similar result was proved by Zhu (Sci. China Math., 2021).","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77594143","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":"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":null,"pages":null},"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}
{"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":null,"pages":null},"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}
. 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.
{"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":null,"pages":null},"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}
. 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.
{"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":null,"pages":null},"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}
{"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":null,"pages":null},"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}
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