Conservation law for the Cauchy-Navier equation of elastodynamics wave via Fourier transform

TL;DR

This paper derives a conservation law for the energy in elastodynamics waves using Fourier analysis, establishing global uniqueness of solutions for the Cauchy-Navier equation in isotropic elastic bodies.

Contribution

It introduces a Fourier-based method to derive the energy conservation law and proves the global uniqueness of solutions for the Cauchy-Navier elastodynamics wave equation.

Findings

Energy conservation law for Cauchy-Navier elastodynamics derived

Global uniqueness of solutions established

Method applicable to isotropic elastic bodies

Abstract

In this paper, we use the method of Fourier analysis to derive the formula of the total energy for the Cauchy problem of the Cauchy-Navier elastodynamics wave equation describing the motion of an isotropic elastic body. The conservation law of the total energy is obtained and consequently, the global uniqueness of the solution to the problem is implied.