RECONSTRUCTION OF A COMPACT MANIFOLD FROM THE SCATTERING DATA OF INTERNAL SOURCES
| Autor: | Teemu Saksala, Matti Lassas, Hanming Zhou |
|---|---|
| Přispěvatelé: | Department of Mathematics and Statistics, Matti Lassas / Principal Investigator, Inverse Problems |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Control and Optimization
Geodesic Riemannian geometry 01 natural sciences symbols.namesake RIEMANNIAN MANIFOLD partial differential equations 111 Mathematics Discrete Mathematics and Combinatorics Pharmacology (medical) DIFFRACTION TRAVEL-TIMES 0101 mathematics Mathematics::Symplectic Geometry Physics Partial differential equation compact manifold with boundary Scattering 010102 general mathematics Mathematical analysis RIGIDITY Riemannian manifold Inverse problem Wave equation METRICS Mathematics::Geometric Topology WAVE-EQUATION 010101 applied mathematics Modeling and Simulation symbols Mathematics::Differential Geometry Convex function Analysis INVERSE PROBLEMS geodesics |
| Popis: | Given a smooth non-trapping compact manifold with strictly convex boundary, we consider an inverse problem of reconstructing the manifold from the scattering data initiated from internal sources. These data consist of the exit directions of geodesics that are emaneted from interior points of the manifold. We show that under certain generic assumption of the metric, the scattering data measured on the boundary determine the Riemannian manifold up to isometry. |
| Databáze: | OpenAIRE |
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