Detail publikace
Global Existence and Blow-up Solutions for a Parabolic Equation with Critical Nonlocal Interactions
ZHANG, J. RADULESCU, V. YANG, M. ZHOU, J.
Originální název
Global Existence and Blow-up Solutions for a Parabolic Equation with Critical Nonlocal Interactions
Typ
článek v časopise ve Web of Science, Jimp
Jazyk
angličtina
Originální abstrakt
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.
Klíčová slova
Nonlocal parabolic equation; Hardy-Littlewood-Sobolev critical exponent; Global existenc; Asymptotic behavior; Finite time blow-up
Autoři
ZHANG, J.; RADULESCU, V.; YANG, M.; ZHOU, J.
Vydáno
26. 3. 2025
Nakladatel
Springer Nature
ISSN
1572-9222
Periodikum
Journal of Dynamics and Differential Equations
Ročník
37
Číslo
1
Stát
Spojené státy americké
Strany od
687
Strany do
725
Strany počet
39
URL
Plný text v Digitální knihovně
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"
}