Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 801-819 |
| Seitenumfang | 19 |
| Fachzeitschrift | SIAM Journal on Mathematical Analysis |
| Jahrgang | 56 |
| Ausgabenummer | 1 |
| Frühes Online-Datum | 16 Jan. 2024 |
| Publikationsstatus | Veröffentlicht - 2024 |
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.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
- Mathematik (insg.)
- Computational Mathematics
- Mathematik (insg.)
- Angewandte Mathematik
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in: SIAM Journal on Mathematical Analysis, Jahrgang 56, Nr. 1, 2024, S. 801-819.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Weakly Nonlinear Geometric Optics for the Westervelt Equation and Recovery of the Nonlinearity
AU - Eptaminitakis, Nikolas
AU - Stefanov, Plamen
N1 - Funding Information: The work of the second author was partially supported by NSF grant DMS-2154489. \dagger Institut fu\"r Differentialgeometrie, Leibniz Universita\"t Hannover, 30167 Hannover, Germany (nikolaos.eptaminitakis@math.uni-hannover.de). \ddagger Department of Mathematics, Purdue University, West Lafayette, IN 47907 USA (stefanov@math. purdue.edu).
PY - 2024
Y1 - 2024
N2 - 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.
AB - 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.
KW - geometric optics
KW - inverse problem
KW - nonlinear optics
KW - Westervelt
UR - http://www.scopus.com/inward/record.url?scp=85183722861&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2208.13945
DO - 10.48550/arXiv.2208.13945
M3 - Article
AN - SCOPUS:85183722861
VL - 56
SP - 801
EP - 819
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
SN - 0036-1410
IS - 1
ER -