Uniform stability of a coupled system of hyperbolic/parabolic PDEs with internal dissipation

Abstract: We study the uniform stability of a coupled system of hyperbolic/parabolic partial differential equations (PDEs) with nonlinear internal dissipation. We analyze both the case of distributed damping on the entire domain, and the case of damping with localised support. In the corresponding stability results, decay rates of weak solutions to the PDE system under consideration are described via the solutions to appropriate nonlinear ordinary differential equations.