Dynamics of a coupled nonlinear wave equations with fractional Laplacian damping and Fourier’s law

Abstract

In this paper, we consider a two-dimensional system of coupled nonlinear wave equations, one of which is subject to fractional Laplacian damping, the linear part of the system is based on Alabau-Boussouira et al. (J Evol Equ 2(2):127–150, 2002. https://doi.org/10.1007/s00028-002-8083-0). In addition, we consider the thermal effect according to Fourier’s Law acting on the system. We prove that the (two-parameters) dynamical system associates the solution of the system is quasi-stable and gradient, which implies the existence of a (two-parameters) family of compact global attractors. A result of regularity is also proven for the attractors, as well as showing that the family of attractors is upper semicontinuous, on the set of parameters.