Publication

Stable determination of X-ray transforms of time dependent potentials from the dynamical Dirichlet-to-Neumann map

Waters, A. M. S., 16-Sep-2014, In : Communications in partial differential equations. 39, 12, p. 2169-2197

Research output: Contribution to journalArticleAcademicpeer-review

APA

Waters, A. M. S. (2014). Stable determination of X-ray transforms of time dependent potentials from the dynamical Dirichlet-to-Neumann map. Communications in partial differential equations, 39(12), 2169-2197. https://doi.org/10.1080/03605302.2014.930486

Author

Waters, Alden Marie Seaburg. / Stable determination of X-ray transforms of time dependent potentials from the dynamical Dirichlet-to-Neumann map. In: Communications in partial differential equations. 2014 ; Vol. 39, No. 12. pp. 2169-2197.

Harvard

Waters, AMS 2014, 'Stable determination of X-ray transforms of time dependent potentials from the dynamical Dirichlet-to-Neumann map', Communications in partial differential equations, vol. 39, no. 12, pp. 2169-2197. https://doi.org/10.1080/03605302.2014.930486

Standard

Stable determination of X-ray transforms of time dependent potentials from the dynamical Dirichlet-to-Neumann map. / Waters, Alden Marie Seaburg.

In: Communications in partial differential equations, Vol. 39, No. 12, 16.09.2014, p. 2169-2197.

Research output: Contribution to journalArticleAcademicpeer-review

Vancouver

Waters AMS. Stable determination of X-ray transforms of time dependent potentials from the dynamical Dirichlet-to-Neumann map. Communications in partial differential equations. 2014 Sep 16;39(12):2169-2197. https://doi.org/10.1080/03605302.2014.930486


BibTeX

@article{572b8c468e424e57bcc16d82fac07518,
title = "Stable determination of X-ray transforms of time dependent potentials from the dynamical Dirichlet-to-Neumann map",
abstract = "We consider compact smooth Riemmanian manifolds with boundary of dimension greater than or equal to two. For the initial-boundary value problem for the wave equation with a lower order term q(t, x), we can recover the X-ray transform of time dependent potentials q(t, x) from the dynamical Dirichlet-to-Neumann map in a stable way. We derive conditional H{\"o}lder stability estimates for the X-ray transform of q(t, x). The essential technique involved is the Gaussian beam Ansatz, and the proofs are done with the minimal assumptions on the geometry for the Ansatz to be well-defined.",
author = "Waters, {Alden Marie Seaburg}",
year = "2014",
month = "9",
day = "16",
doi = "10.1080/03605302.2014.930486",
language = "English",
volume = "39",
pages = "2169--2197",
journal = "Communications in partial differential equations",
issn = "0360-5302",
publisher = "Taylor & Francis Group",
number = "12",

}

RIS

TY - JOUR

T1 - Stable determination of X-ray transforms of time dependent potentials from the dynamical Dirichlet-to-Neumann map

AU - Waters, Alden Marie Seaburg

PY - 2014/9/16

Y1 - 2014/9/16

N2 - We consider compact smooth Riemmanian manifolds with boundary of dimension greater than or equal to two. For the initial-boundary value problem for the wave equation with a lower order term q(t, x), we can recover the X-ray transform of time dependent potentials q(t, x) from the dynamical Dirichlet-to-Neumann map in a stable way. We derive conditional Hölder stability estimates for the X-ray transform of q(t, x). The essential technique involved is the Gaussian beam Ansatz, and the proofs are done with the minimal assumptions on the geometry for the Ansatz to be well-defined.

AB - We consider compact smooth Riemmanian manifolds with boundary of dimension greater than or equal to two. For the initial-boundary value problem for the wave equation with a lower order term q(t, x), we can recover the X-ray transform of time dependent potentials q(t, x) from the dynamical Dirichlet-to-Neumann map in a stable way. We derive conditional Hölder stability estimates for the X-ray transform of q(t, x). The essential technique involved is the Gaussian beam Ansatz, and the proofs are done with the minimal assumptions on the geometry for the Ansatz to be well-defined.

U2 - 10.1080/03605302.2014.930486

DO - 10.1080/03605302.2014.930486

M3 - Article

VL - 39

SP - 2169

EP - 2197

JO - Communications in partial differential equations

JF - Communications in partial differential equations

SN - 0360-5302

IS - 12

ER -

ID: 84197478