# Anisotropic thermo-elasticity in 2D -- Part I: A unified approach

## TL;DR

This paper develops a unified mathematical framework for analyzing anisotropic thermo-elasticity in two dimensions, focusing on decay rates of solutions using diagonalization techniques.

## Contribution

It introduces a novel approach to study anisotropic thermo-elastic systems in 2D by analyzing characteristic roots for decay properties.

## Key findings

- Established $L^p$--$L^q$ decay rates for solutions
- Developed diagonalization techniques for characteristic roots
- Provided tools for future analysis of anisotropic thermo-elasticity

## Abstract

In this note we develop tools and techniques for the treatment of anisotropic thermo-elasticity in two space dimensions. We use a diagonalisation technique to obtain properties of the characteristic roots of the full symbol of the system in order to prove $L^p$--$L^q$ decay rates for its solutions.