Indirect stabilization of semilinear coupled wave systems

TL;DR

This paper investigates the exponential stabilization of coupled semilinear wave systems with internal damping, demonstrating decay under geometric control conditions for subcritical, defocusing, analytic nonlinearities.

Contribution

It establishes exponential energy decay for coupled wave equations with internal damping under geometric control, extending stabilization results to nonlinear, coupled systems.

Findings

Exponential decay rate of energy is proven.

Stability holds under geometric control conditions.

Results apply to subcritical, defocusing, analytic nonlinearities.

Abstract

In this paper, we study the indirect stabilization problem for a system of two coupled semilinear wave equations with internal damping in a bounded domain in $\mathbb{R}^3$. The nonlinearity is assumed to be subcritical, defocusing and analytic. Under geometric control condition on both coupling and damping regions, we establish the exponential energy decay rate.