Indirect stabilization of weakly coupled systems with hybrid boundary conditions

TL;DR

This paper studies the stability of weakly coupled evolution systems with hybrid boundary conditions, proving polynomial decay of energy and providing explicit estimates, with applications to coupled wave equations.

Contribution

It introduces new compatibility assumptions for stability analysis and achieves a full range of decay rates using interpolation techniques.

Findings

Polynomial decay of energy established

Explicit estimates with respect to initial data provided

Applications to coupled wave equations with hybrid boundary conditions

Abstract

We investigate stability properties of indirectly damped systems of evolution equations in Hilbert spaces, under new compatibility assumptions. We prove polynomial decay for the energy of solutions and optimize our results by interpolation techniques, obtaining a full range of power-like decay rates. In particular, we give explicit estimates with respect to the initial data. We discuss several applications to hyperbolic systems with {\em hybrid} boundary conditions, including the coupling of two wave equations subject to Dirichlet and Robin type boundary conditions, respectively.