On the existence of the Moller wave operator for wave equations with small dissipative terms

TL;DR

This paper extends previous results on wave equations with small dissipative terms by explicitly constructing the wave operator using a simplified diagonalization and ODE techniques, providing a new approach to scattering theory.

Contribution

It introduces an explicit construction of the wave operator for dissipative wave equations using a simplified diagonalization method and ODE techniques, extending Mochizuki's earlier work.

Findings

Explicit wave operator construction for small dissipative wave equations

Extension of Mochizuki's scattering operator results

Method based on simplified diagonalization and ODE techniques

Abstract

The aim of this short note is to reconsider and to extend a former result of K. Mochizuki on the existence of the scattering operator for wave equations with small dissipative terms. Contrary to the approach used by Mochizuki we construct the wave operator explicitly in terms of the parametrix construction obtained by a (simplified) diagonalization procedure. The method is based on ODE techniques.