Inverse Problem with the Boundary Distance Functions on Finsler Manifolds in Anisotropic Elasticity
Abstract
The speaker and his collaborators consider the collection of all boundary distance functions of a smooth compact Finsler manifold with smooth boundary as the data. They show that these determine its topological and differential structures up to isometry. In addition, they present a construction of a fiberwise open subset of the tangent bundle and show that the collection of all boundary distance functions determine the Finsler function in this set but not in the exterior of this set unless the Finsler function is fiberwise analytic. This function is fiberwise analytic when it arises from linear (anisotropic) elasticity. They then briefly present the generalized Dix inverse problem on a Finsler manifold from seismology using certain sphere data in a given open subset of the manifold as the data, and discuss its recovery in the neighborhood of any geodesic through the open set.
This is a joint research with Joonas ILMAVIRTA, Matti LASSAS and Teemu SAKSALA.
About the speaker
Prof. Maarten V de Hoop obtained his PhD in Technical Sciences at Delft University of Technology in 1992. He was a Senior Research Scientist and Program Leader at Schlumberger Cambridge Research from 1992 to 1995. He then joined the faculty of the Department of Mathematical and Computer Sciences at the Colorado School of Mines in 1995, before he moved to Purdue University as a Professor of Mathematics and of Earth, Atmospheric, and Planetary Sciences in 2005. He joined Rice University in 2015 and is currently the Simons Chair in Computational and Applied Mathematics and Earth Science.
Prof. de Hoop’s research interests include scattering, imaging and inverse problems, theoretical and computational seismology, and geodesy. He is a member of the Society for Industrial and Applied Mathematics, the American Mathematical Society, the American Geophysical Union and the Society of Exploration Geophysicists. He is also a Fellow of the Institute of Physics since 2001.
About the program
For more information, please refer to the program website at http://iasprogram.ust.hk/inverseproblems.
