Well-posedness and stability results for a class of nonlinear fourth-order wave equation with variable-exponents

Document Type : Research Paper

Authors

Department of Sciences and Technology, Laboratory of Applied Mathematics and History and Didactics of Mathematics (LAMAHIS), University of 20 August 1955, Skikda, Algeria

Abstract

In this paper, we consider a class of nonlinear fourth-order wave equation with damping and source terms of variable-exponent types. First, by the Faedo-Galerkin approximation method with positive initial energy and suitable conditions on the variable exponents $m(.)$ and $r(.) $, we established the local existence. We also prove that the local solution is global. Finally, the stability estimate of the solution was obtained by using the Komornik inequality

Keywords

Volume 14, Issue 1
January 2023
Pages 1769-1785
  • Receive Date: 09 May 2022
  • Revise Date: 27 September 2022
  • Accept Date: 26 November 2022