On the well posedness and stability of an (α,β)-Laplacian nonlinearly damped coupled system with source terms of strong nonlinearities

Abstract

The paper deals with the local and global well posedness of coupled system of (α,β)-Laplacian type of wave equations with initial and Dirichlet-boundary conditions and variable exponents of nonlinearity. Furthermore, explicit decay rates of the solutions are established, under suitable assumptions on the parameters of the problem. This work generalizes all the existing results (in the literature) that concern “similar” systems with α,β∈{1,2} to the case where β≥α≥1.