Global Existence and Blow-up Solutions for a Parabolic Equation with Critical Nonlocal Interactions
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Date
2025-03-26
Authors
Zhang, Jian
Radulescu, Vicentiu
Yang, Minbo
Zhou, Jiazheng
ORCID
0000-0003-4615-5537Advisor
Referee
Mark
Journal Title
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Volume Title
Publisher
Springer Nature
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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 J(mu)(u0) < 0 and decay rate of H-0(1) and L-2-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.
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Citation
Journal of Dynamics and Differential Equations. 2025, vol. 37, issue 1, p. 687-725.
https://link.springer.com/article/10.1007/s10884-023-10278-y
https://link.springer.com/article/10.1007/s10884-023-10278-y
Document type
Peer-reviewed
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Language of document
en