Publication detail
Global Existence and Blow-up Solutions for a Parabolic Equation with Critical Nonlocal Interactions
ZHANG, J. RADULESCU, V. YANG, M. ZHOU, J.
Original Title
Global Existence and Blow-up Solutions for a Parabolic Equation with Critical Nonlocal Interactions
Type
journal article in Web of Science
Language
English
Original 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.
Keywords
Nonlocal parabolic equation; Hardy-Littlewood-Sobolev critical exponent; Global existenc; Asymptotic behavior; Finite time blow-up
Authors
ZHANG, J.; RADULESCU, V.; YANG, M.; ZHOU, J.
Released
26. 3. 2025
Publisher
Springer Nature
ISBN
1572-9222
Periodical
Journal of Dynamics and Differential Equations
Year of study
37
Number
1
State
United States of America
Pages from
687
Pages to
725
Pages count
39
URL
Full text in the Digital Library
BibTex
@article{BUT185760,
author="Jian {Zhang} and Vicentiu {Radulescu} and Minbo {Yang} and Jiazheng {Zhou}",
title="Global Existence and Blow-up Solutions for a Parabolic Equation with Critical Nonlocal Interactions",
journal="Journal of Dynamics and Differential Equations",
year="2025",
volume="37",
number="1",
pages="687--725",
doi="10.1007/s10884-023-10278-y",
issn="1572-9222",
url="https://link.springer.com/article/10.1007/s10884-023-10278-y"
}