DeepAI AI Chat
Log In Sign Up

On the simultanenous identification of two space dependent coefficients in a quasilinear wave equation

by   Barbara Kaltenbacher, et al.

This paper considers the Westervelt equation, one of the most widely used models in nonlinear acoustics, and seeks to recover two spatially-dependent parameters of physical importance from time-trace boundary measurements. Specifically, these are the nonlinearity parameter κ(x) often referred to as B/A in the acoustics literature and the wave speed c_0(x). The determination of the spatial change in these quantities can be used as a means of imaging. We consider identifiability from one or two boundary measurements as relevant in these applications. More precisely, we provide results on local uniqueness of κ(x) from a single observation and on simultaneous identifiability of κ(x) and c_0(x) from two measurements. For a reformulation of the problem in terms of the squared slowness =1/c_0^2 and the combined coefficient =κ/c_0^2 we devise a frozen Newton method and prove its convergence. The effectiveness (and limitations) of this iterative scheme are demonstrated by numerical examples.


page 1

page 2

page 3

page 4


On the simultaneous recovery of the conductivity and the nonlinear reaction term in a parabolic equation

This paper considers the inverse problem of recovering both the unknown,...

On an inverse problem of nonlinear imaging with fractional damping

This paper considers the attenuated Westervelt equation in pressure form...

On the identification of the nonlinearity parameter in the Westervelt equation from boundary measurements

We consider an undetermined coefficient inverse problem for a non- linea...

Computational identification of the lowest space-wise dependent coefficient of a parabolic equation

In the present work, we consider a nonlinear inverse problem of identify...

Inverse conductivity equation with internal data

This paper concerns the reconstruction of a scalar coefficient of a seco...

On uniqueness and stable estimation of multiple parameters in the Cahn-Hilliard equation

We consider the identifiability and stable numerical estimation of multi...

Nonlinearity parameter imaging in the frequency domain

Nonlinearity parameter tomography leads to the problem of identifying a ...