# Dissipative structure and diffusion phenomena for doubly dissipative elastic waves in two space dimensions

## TL;DR

This paper investigates the behavior of doubly dissipative elastic waves in two dimensions, deriving energy estimates and diffusion phenomena, and introduces a new threshold that influences the diffusion structure based on initial data assumptions.

## Contribution

It presents new insights into the diffusion phenomena of doubly dissipative elastic waves, including the derivation of energy estimates and the identification of a novel diffusion threshold.

## Key findings

- Energy estimates for doubly dissipative elastic waves
- Diffusion phenomena characterized under various initial data assumptions
- Introduction of a new threshold influencing diffusion structure

## Abstract

In this paper we study the Cauchy problem for doubly dissipative elastic waves in two space dimensions, where the damping terms consist of two different friction or structural damping. We derive energy estimates and diffusion phenomena with different assumptions on initial data. Particularly, we find the dominant influence on diffusion phenomena by introducing a new threshold of diffusion structure.