Document Type : Research Paper

Authors

• Amar Ouaoua
• Wissem Boughamsa

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

• Nonlinear fourth-order wave equation
• Faedo-Galerkin method
• Global existence
• Stability result