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

Document Type : Research Paper


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


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


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