Methods and Applications of Analysis
Volume 28 (2021)
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
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.
finitely degenerate coupled parabolic systems, global existence, blow-up, asymptotic behavior
2010 Mathematics Subject Classification
Primary 35K51, 35K58, 35K65. Secondary 35B44.
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