A coupled system of Laplacian and bi-Laplacian equations with nonlinear dampings and source terms of variable-exponents nonlinearities: Existence, uniqueness, blow-up and a large-time asymptotic behavior

Salim A. Messaoudi, Mohammad M. Al-Gharabli, Adel M. Al-Mahdi*, Mohammed A. Al-Osta

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

In this paper, we consider a coupled system of Laplacian and bi-Laplacian equations with nonlinear dampings and source terms of variable-exponents nonlinearities. This system is supplemented with initial and mixed boundary conditions. First, we establish the existence and uniqueness results of a weak solution, under suitable assumptions on the variable exponents. Second, we show that the solutions with positive-initial energy blow-up in a finite time. Finally, we establish the global existence as well as the energy decay results of the solutions, using the stable-set and the multiplier methods, under appropriate conditions on the variable exponents and the initial data.

Original languageEnglish
Pages (from-to)7933-7966
Number of pages34
JournalAIMS Mathematics
Volume8
Issue number4
DOIs
StatePublished - 2023

Bibliographical note

Publisher Copyright:
© 2023 the Author(s), licensee AIMS Press.

Keywords

  • biharmonic equations
  • blow-up
  • coupled system
  • global existence
  • stability
  • variable exponent

ASJC Scopus subject areas

  • General Mathematics

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