Exponential decay for a Klein–Gordon–Schrödinger system with locally distributed damping

Abstract

A coupled damped Klein–Gordon–Schrödinger equations are considered where $\Omega$ is a bounded domain of $\mathbb{R}^{2},$ with smooth boundary $\Gamma$ and $\omega$ is a neighbourhood of $\partial \Omega$ satisfying the geometric control condition. The aim of the paper is to prove the existence, uniqueness and uniform decay for the solutions.

Keywords

• klein–gordon–schrödinger
• localized damping
• exponential stability
• asymptotic behavior
• existence and uniqueness