On a nonlinear system of plate equations with variable exponent nonlinearity and logarithmic source terms: Existence and stability results

Adel M. Al-Mahdi*, Mohammad M. Al-Gharabli, Nasser Eddine Tatar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

In this paper, we consider a coupling non-linear system of two plate equations with logarithmic source terms. First, we study the local existence of solutions of the system using the Faedo-Galerkin method and Banach fixed point theorem. Second, we prove the global existence of solutions of the system by using the potential wells. Finally, using the multiplier method, we establish an exponential decay result for the energy of solutions of the system. Some conditions on the variable exponents that appear in the coupling functions and the involved constants that appear in the source terms are determined to ensure the existence and stability of solutions of the system. A series of lemmas and theorems have been proved and used to overcome the difficulties caused by the variable exponent and the logarithmic nonlinearities. Our result generalizes some earlier related results in the literature from the case of only constant exponent of the nonlinear internal forcing terms to the case of variable exponent and logarithmic source terms, which is more useful from the physical point of view and needed in several applications.

Original languageEnglish
Pages (from-to)19971-19992
Number of pages22
JournalAIMS Mathematics
Volume8
Issue number9
DOIs
StatePublished - 2023

Bibliographical note

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

Keywords

  • Banach fixed point theorem
  • Galerkin method
  • exponential decay
  • logarithmic Sobolev inequality
  • logarithmic nonlinearity
  • multiplier method
  • plate equations
  • variable-exponent

ASJC Scopus subject areas

  • General Mathematics

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