Stabilization for degenerate equations with drift and small singular term

TL;DR

This paper studies the stabilization of a one-dimensional degenerate and singular wave equation with drift, establishing conditions for exponential decay of solutions despite the equation's degeneracy and non-divergence form.

Contribution

It introduces new conditions for uniform exponential decay in degenerate/singular wave equations with drift and non-divergence operators.

Findings

Established exponential decay conditions for solutions

Analyzed wave equations with degeneracy and singularity

Provided boundary damping strategies for stabilization

Abstract

We consider a degenerate/singular wave equation in one dimension, with drift and in presence of a leading operator which is not in divergence form. We impose a homogeneous Dirichlet boundary condition where the degeneracy occurs and a boundary damping at the other endpoint. We provide some conditions for the uniform exponential decay of solutions for the associated Cauchy problem.