Determination of the density in a nonlinear elastic wave equation

TL;DR

This paper extends previous work on inverse boundary problems for nonlinear elastic waves, demonstrating that all coefficients, including density, can be uniquely recovered from boundary measurements under certain geometric conditions.

Contribution

It proves the unique recovery of the density and other coefficients in a nonlinear elastic wave equation from boundary data, advancing inverse problem theory.

Findings

All linear and nonlinear coefficients can be recovered from boundary measurements.

Density can be uniquely determined under geometric conditions.

The results extend previous inverse boundary value problem solutions.

Abstract

This is a continuation of our study [Uhlmann-Zhai, JMPA, 2021] on an inverse boundary value problem for a nonlinear elastic wave equation. We prove that all the linear and nonlinear coefficients can be recovered from the displacement-to-traction map, including the density, under some natural geometric conditions on the wavespeeds.