Decay estimates for a class of wave equations

TL;DR

This paper develops a unified approach to derive decay estimates for a class of dispersive wave equations, simplifying and improving results for Klein-Gordon and beam equations.

Contribution

It introduces a unified method for decay estimates applicable to various dispersive equations, enhancing previous results for specific cases.

Findings

Simplified decay estimates for Klein-Gordon and beam equations

Improved decay rate bounds for solutions

Unified framework for dispersive wave decay analysis

Abstract

In this paper we use a unified way studying the decay estimate for a class of dispersive semigroup given by $e^{it\phi(\sqrt{-\Delta})}$, where $\phi: \mathbb{R}^+\to \mathbb{R}$ is smooth away from the origin. Especially, the decay estimates for the solutions of the Klein-Gordon equation and the beam equation are simplified and slightly improved.