Decay for solutions of a nonlinear damped wave equation with variable-exponent nonlinearities

In this paper, we consider the following nonlinear waveequation with variable exponents: utt−div(|∇u|r(⋅)−2∇u)+|ut|m(⋅)−2ut=0.By using a lemma by Komornik, we prove the decay estimates for the solution under suitable assumptions on the variable exponents m,r and the initial data. We also give two numerical applications to illustrate our theoretical results.