Título:	Global existence and blow-up solutions for a parabolic equation with critical nonlocal interactions
Autor(es):	Zhang, Jian Rădulescu, Vicentiu D. Yang, Minbo Zhou, Jiazheng
Afiliação do autor:	Zhejiang Normal University, Department of Mathematics Zhejiang Normal University, Department of Mathematics AGH University of Science and Technology, Faculty of Applied Mathematics University of Craiova, Department of Mathematics Brno University of Technology, Faculty of Electrical Engineering and Communication Zhejiang Normal University, Department of Mathematics Universidade de Brasília, Departmento de Matemática
Data de publicação:	Mar-2025
Editora:	Springer Science and Business Media LLC
Referência:	ZHANG, Jian et al. Global existence and blow-up solutions for a parabolic equation with critical nonlocal interactions. Journal of Dynamics and Differential Equations, [S. l.], v. 37, n. 1, p. 687-725, 2025. DOI: https://doi.org/10.1007/s10884-023-10278-y. Disponível em: https://link.springer.com/article/10.1007/s10884-023-10278-y. Acesso em: 25 ago. 2026.
Abstract:	In this paper, we study the initial boundary value problem for the nonlocal parabolic equation with the Hardy–Littlewood–Sobolev critical exponent on a bounded domain. We are concerned with the long time behaviors of solutions when the initial energy is low, critical or high. More precisely, by using the modified potential well method, we obtain global existence and blow-up of solutions when the initial energy is low or critical, and it is proved that the global solutions are classical. Moreover, we obtain an upper bound of blow-up time for and decay rate of and -norm of the global solutions. When the initial energy is high, we derive some sufficient conditions for global existence and blow-up of solutions. In addition, we are going to consider the asymptotic behavior of global solutions, which is similar to the Palais-Smale (PS for short) sequence of stationary equation.
Unidade Acadêmica:	Instituto de Ciências Exatas (IE) Departamento de Matemática (IE MAT)
Licença:	OpenAccess This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
DOI:	https://doi.org/10.1007/s10884-023-10278-y
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