Local energy decay for the wave equation with nonlinear time dependent damping

TL;DR

This paper studies how local energy in a wave equation with nonlinear, time-dependent damping decays over time in an exterior domain, using microlocal geometric conditions and nonlinear differential equations.

Contribution

It introduces a novel approach to analyze decay rates for wave equations with nonlinear, time-dependent damping under microlocal geometric conditions.

Findings

Decay rates characterized by solving a nonlinear non-autonomous differential equation

Established decay estimates for local energy in exterior domains

Applicable to odd-dimensional spaces

Abstract

This paper addresses a wave equation on a exterior domain in R^{d}(d odd) with nonlinear time dependent dissipation. Under a microlocal geometric condition we prove that the decay rates of the local energy functional are obtained by solving a nonlinear non-autonomous differential equation.