Exponential Energy Decay for Damped Klein-Gordon Equation with Nonlinearities of Arbitrary Growth

TL;DR

This paper proves that the total energy of a nonlinear Klein-Gordon equation with damping decays exponentially over time, applicable in unbounded domains or exterior of obstacles, regardless of the nonlinearity's growth.

Contribution

It establishes uniform exponential energy decay for the nonlinear Klein-Gordon equation with damping, extending results to arbitrary nonlinear growth and complex geometries.

Findings

Energy decays exponentially over time.

Decay holds in unbounded domains and exterior of obstacles.

Applicable to nonlinearities of arbitrary growth.

Abstract

We derive a uniform exponential decay of the total energy for the nonlinear Klein-Gordon equation with a damping around spatial infinity in the whole space or in the exterior of a star shaped obstacle.