Decay result in a problem of a nonlinearly damped wave equation with variable exponent

Abstract

In this work we study a wave equation with a nonlinear time dependent frictional damping of variable exponent type. The existence and uniqueness results are established using Fadeo-Galerkin approximation method. We also exploit the Komornik lemma to prove the uniform stability result for the energy associated to the solution of the problem under consideration.

Keywords

• viscoelasticity
• relaxation function
• general decay
• logarithmic nonlinearity
• variable exponent