Weakly Nonlinear Geometric Optics for the Westervelt Equation and Recovery of the Nonlinearity

authored by

Nikolas Eptaminitakis, Plamen Stefanov

Abstract

We study the nondiffusive Westervelt equation in the weakly nonlinear regime and show that the leading profile equation is of Burgers' type. We show that a compactly supported nonlinearity coefficient α can be reconstructed from the tilt of the transmitted high frequency wave packets sent from different directions, by demonstrating that those tilts are proportional to the X-ray transform of α.

Organisation(s)

Institute of Differential Geometry

External Organisation(s)

Purdue University

Type

Article

Journal

SIAM Journal on Mathematical Analysis

Volume

56

Pages

801-819

No. of pages

19

ISSN

0036-1410

Publication date

2024

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Analysis, Computational Mathematics, Applied Mathematics

Electronic version(s)

https://doi.org/10.48550/arXiv.2208.13945 (Access: Open)
https://doi.org/10.1137/22M1543379 (Access: Closed)