On polynomial stability of coupled partial differential equations in 1d

Abstract

We study the well-posedness and asymptotic behaviour of selected PDE–PDE and PDE–ODE systems on one-dimensional spatial domains, namely a boundary coupled wave–heat system and a wave equation with a dynamic boundary condition. We prove well-posedness of the models and derive rational decay rates for the energy using an approach where the coupled systems are formulated as feedback interconnections of impedance passive regular linear systems.