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

https://link.springer.com/article/10.1007/s10884-023-10278-y

Plný text v Digitální knihovně

http://hdl.handle.net/11012/251189

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"
}