6533b7d6fe1ef96bd1265cf0

RESEARCH PRODUCT

Recovery of time-dependent coefficients from boundary data for hyperbolic equations

Ali FeizmohammadiLauri OksanenJoonas IlmavirtaYavar Kian

subject

GeodesicDirichlet-to-Neumann maplight ray transformmagnetic potentialBoundary (topology)CALDERON PROBLEM01 natural sciencesGaussian beamMathematics - Analysis of PDEsFOS: Mathematics111 Mathematics[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]Uniqueness0101 mathematicsMathematics::Symplectic GeometryMathematical PhysicsMathematicsX-ray transformSTABILITYinverse problemsMathematical analysisStatistical and Nonlinear PhysicsRiemannian manifoldX-RAY TRANSFORMWave equationMathematics::Geometric TopologyManifoldTENSOR-FIELDS010101 applied mathematicsUNIQUE CONTINUATIONGeometry and TopologyMathematics::Differential GeometryWAVE-EQUATIONSHyperbolic partial differential equationAnalysis of PDEs (math.AP)

description

We study uniqueness of the recovery of a time-dependent magnetic vector-valued potential and an electric scalar-valued potential on a Riemannian manifold from the knowledge of the Dirichlet to Neumann map of a hyperbolic equation. The Cauchy data is observed on time-like parts of the space-time boundary and uniqueness is proved up to the natural gauge for the problem. The proof is based on Gaussian beams and inversion of the light ray transform on Lorentzian manifolds under the assumptions that the Lorentzian manifold is a product of a Riemannian manifold with a time interval and that the geodesic ray transform is invertible on the Riemannian manifold.

yearjournalcountryeditionlanguage
2019-01-14
10.4171/jst/367http://hdl.handle.net/10138/337891