Methods and Applications of Analysis

Volume 28 (2021)

Number 2

Special issue dedicated to Professor Ling Hsiao on the occasion of her 80th birthday, Part I

Guest editors: Qiangchang Ju (Institute of Applied Physics and Computational Mathematics, Beijing), Hailiang Li (Capital Normal University, Beijing), Tao Luo (City University of Hong Kong), and Zhouping Xin (Chinese University of Hong Kong)

Global existence, exponential decay and finite time blow-up for a class of finitely degenerate coupled parabolic systems

Pages: 173 – 194

DOI: https://dx.doi.org/10.4310/MAA.2021.v28.n2.a4

Authors

Hua Chen (School of Mathematics and Statistics, Wuhan University, Wuhan, China)

Jing Wang (School of Mathematics and Statistics, Wuhan University, Wuhan, China)

Huiyang Xu (School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, China)

Abstract

In this paper, we study the initial-boundary value problem for finitely degenerate coupled parabolic systems. Using potential well method, we first prove the invariance of some sets and vacuum isolating of solutions. Then, by the Galerkin method, we obtain the global existence and finite time blow-up of solutions with low initial energy and critical initial energy and discuss the asymptotic behavior of the solutions.

Keywords

finitely degenerate coupled parabolic systems, global existence, blow-up, asymptotic behavior

2010 Mathematics Subject Classification

Primary 35K51, 35K58, 35K65. Secondary 35B44.

Full Text (PDF format)

This work is supported by the NSFC under the grants 11631011, 1213000191 and 12101194.

Received 27 April 2020

Accepted 7 August 2020

Published 10 June 2022