Stability for degenerate wave equations with drift under simultaneous degenerate damping

TL;DR

This paper investigates the stability of degenerate wave equations with drift and damping, establishing exponential decay results for both single and coupled systems with degeneracies and transmission conditions.

Contribution

It provides new exponential stability results for degenerate wave equations with drift and damping, including coupled systems with transmission conditions.

Findings

Exponential stability for degenerate wave equations with damping and drift.

Stability results for coupled degenerate and non-degenerate wave systems.

Analysis under simultaneous degeneracy and damping conditions.

Abstract

In this paper we study the stability of two different problems. The first one is a one-dimensional degenerate wave equation with degenerate damping, incorporating a drift term and a leading operator in non-divergence form. In the second problem we consider a system that couples degenerate and non-degenerate wave equations, connected through transmission, and subject to a single dissipation law at the boundary of the non-degenerate equation. In both scenarios, we derive exponential stability results.