On Polynomial Stability of Coupled Partial Differential Equations in 1D

TL;DR

This paper investigates the stability and decay rates of coupled PDE systems in one dimension, establishing well-posedness and energy decay using impedance passive system frameworks.

Contribution

It introduces a novel approach to analyze coupled PDE-ODE and PDE-PDE systems via feedback interconnections of impedance passive systems, providing new stability results.

Findings

Proved well-posedness of boundary coupled wave-heat and wave systems.

Derived rational decay rates for the energy of the systems.

Established a framework for stability analysis using impedance passivity.

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.