Asymptotic Profiles for wave equations with strong damping

TL;DR

This paper analyzes the long-term behavior of solutions to strongly damped wave equations in multi-dimensional space, deriving their asymptotic profiles using weighted $L^{1,1}$ data and a specific analytical method.

Contribution

It introduces a new approach to derive asymptotic profiles for strongly damped wave equations with weighted $L^{1,1}$ data.

Findings

Asymptotic profiles of solutions are characterized.

Method applicable to equations with weighted $L^{1,1}$ data.

Provides insights into the decay behavior of solutions.

Abstract

We consider the Cauchy problem in ${\bf R}^{n}$ for strongly damped wave equations. We derive asymptotic profiles of these solutions with weighted $L^{1,1}({\bf R}^{n})$ data by using a method introduced in [10].