Stability results of locally coupled wave equations with local Kelvin-Voigt damping: Cases when the supports of damping and coupling coefficients are disjoint

TL;DR

This paper investigates the stability of coupled wave equations with local Kelvin-Voigt damping, especially when damping and coupling regions do not overlap, providing new stability results in both one and multiple dimensions.

Contribution

It establishes well-posedness and stability results for coupled wave systems with disjoint damping and coupling supports, extending previous work to multi-dimensional cases.

Findings

Proved well-posedness and strong stability in 1D systems.

Established polynomial stability under certain conditions.

Achieved stability results in multi-dimensional systems with geometric control conditions.

Abstract

In this paper, we study the direct/indirect stability of locally coupled wave equations with local Kelvin-Voigt dampings/damping and by assuming that the supports of the dampings and the coupling coefficients are disjoint. First, we prove the well-posedness, strong stability, and polynomial stability for some one dimensional coupled systems. Moreover, under some geometric control condition, we prove the well-posedness and strong stability in the multi-dimensional case.