Uniform energy decay for wave equations with unbounded damping coefficients

TL;DR

This paper establishes uniform energy decay for wave equations with unbounded damping coefficients in the whole space, providing existence results without requiring compact support or finite propagation speed assumptions.

Contribution

It introduces a novel approach to analyze wave equations with unbounded damping, deriving decay estimates and existence results without strong initial data restrictions.

Findings

Uniform total energy decay estimates are derived.

Existence of weak solutions is established without compact support assumptions.

The method handles essential unbounded damping coefficients.

Abstract

We consider the Cauchy problem for wave equations with unbounded damping coefficients in the whole space. For a general class of unbounded damping coefficients, we derive uniform total energy decay estimates together with a unique existence result of a weak solution. In this case we never impose strong assumptions such as compactness of the support of the initial data. This means that we never rely on the finite propagation speed property of the solution, and we try to deal with an essential unbounded coefficient case.