Moment conditions and lower bounds in expanding solutions of wave equations with double damping terms

TL;DR

This paper derives higher order asymptotic expansions for solutions to wave equations with damping, highlighting differences from heat equations and establishing lower bounds to confirm the optimality of these expansions.

Contribution

It provides new higher order asymptotic expansions for damped wave equations and analyzes the diffusion phenomena with weighted initial data.

Findings

Higher order asymptotic expansions obtained

Differences from heat equation solutions identified

Lower bounds established for optimality

Abstract

In this report we obtain higher order asymptotic expansions of solutions to wave equations with frictional and viscoelastic damping terms. Although the diffusion phenomena are dominant, differences between the solutions we deal with and those of heat equations can be seen by comparing the second order expansions of them. In order to analyze such effects we consider the weighted L1 initial data. We also give some lower bounds which show the optimality of obtained expansions.