Global existence and nonexistence for a class of finitely degenerate coupled parabolic systems with high initial energy level

Yuxuan Chen; Jiangbo Han

doi:10.3934/dcdss.2021109

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2021, Volume 14, Issue 12: 4179-4200. Doi: 10.3934/dcdss.2021109 open access

This issue Previous Article Existence of a solution of discrete Emden-Fowler equation caused by continuous equation Next Article Global well-posedness for the Cauchy problem of generalized Boussinesq equations in the control problem regarding initial data

Global existence and nonexistence for a class of finitely degenerate coupled parabolic systems with high initial energy level

Yuxuan Chen and
Jiangbo Han^,

College of Mathematical Sciences, Harbin Engineering University, Heilongjiang, Harbin 150001, China

^* Corresponding author: Jiangbo Han
^* Corresponding author: Jiangbo Han

Received: June 30, 2021

Revised: July 31, 2021

Early access: October 2021

Published: December 2021

The first author is supported by the NSFHPC under the grants LH2021A001

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In this paper, we consider a class of finitely degenerate coupled parabolic systems. At high initial energy level $ J(u_{0}) > d $, we present a new sufficient condition to describe the global existence and nonexistence of solutions for problem (1)-(4) respectively. Moreover, by applying the Levine's concavity method, we give some affirmative answers to finite time blow up of solutions at arbitrary positive initial energy $ J(u_{0}) > 0 $, including the estimate of upper bound of blowup time.

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Mathematics Subject Classification: Primary: 35K20, 35K55; Secondary: 35A01, 35D30.

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