On the decay of solutions of a damped quasilinear wave equation with variable‐exponent nonlinearities

In this work, we consider the following nonlinear wave equation with variable exponents:u t t − d i v ( | ∇ u | r ( . ) − 2 ∇ u ) − Δ u t + | u t| m ( . ) − 2u t = 0 , in Ω × ( 0 , T ) , where Ω is a bounded domain, T > 0 , and m ( . ) and r ( . ) are continuous functions. We will establish several decay results depending on the range of the variable exponents m and r .