Note on a nonlinear coupled 4th-order parabolic problem

This paper deals with the coupled fourth-order parabolic equations, subject to Dirichlet or Navier boundary conditions. We combine the generalized potential well method, the concave method, with the auxiliary methods to classify the initial energy about the existence of blow-up solutions and global...

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Bibliographic Details
Published inJournal of Differential Equations Vol. 395; pp. 153 - 180
Main Authors Li, Fengjie, Li, Ping
Format Journal Article
LanguageEnglish
Published Elsevier Inc 25.06.2024
Subjects
Blow-up rate
Blow-up time
Coupled fourth-order parabolic equations
Decay estimate
Global existence
Blow-up time
Decay estimate
35B44
Global existence
35K25
35B40
Coupled fourth-order parabolic equations
Blow-up rate
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Summary:This paper deals with the coupled fourth-order parabolic equations, subject to Dirichlet or Navier boundary conditions. We combine the generalized potential well method, the concave method, with the auxiliary methods to classify the initial energy about the existence of blow-up solutions and global solutions. Moreover, the decay estimate of global solutions and the bounds of blow-up time and rate are determined, respectively.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2024.02.045