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

  • * Corresponding author: Jiangbo Han

    * Corresponding author: Jiangbo Han
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.

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


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