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

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

Number

State

United States of America

Pages from

687

Pages to

725

Pages count

URL

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

Full text in the Digital Library

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"
}