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

verfasst von

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.

Organisationseinheit(en)

Institut für Differentialgeometrie

Externe Organisation(en)

Purdue University

Typ

Artikel

Journal

SIAM Journal on Mathematical Analysis

Band

56

Seiten

801-819

Anzahl der Seiten

19

ISSN

0036-1410

Publikationsdatum

2024

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Analysis, Computational Mathematics, Angewandte Mathematik

Elektronische Version(en)

https://doi.org/10.48550/arXiv.2208.13945 (Zugang: Offen)
https://doi.org/10.1137/22M1543379 (Zugang: Geschlossen)