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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

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  • Stable Determination of X Ray Transforms of Time Dependent Potentials from Partial Boundary Data(2)

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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.
Original languageEnglish
Pages (from-to)2169-2197
JournalCommunications in partial differential equations
Volume39
Issue number12
Publication statusPublished - 16-Sep-2014
Externally publishedYes

ID: 84197478