Lauri Oksanen (UCL)
Inverse problem for the wave equation with Dirichlet data and Neumann
data on disjoint sets
Abstract:
We consider the inverse boundary value problem that arises when a
spatially variable sound speed inside a body is probed using acoustic
waves that are produced and recorded on the surface of the body. This
serves as a model problem e.g. for seismic imaging. In this talk, we
consider the wave equation for the Laplace operator of a smooth
compact Riemannian manifold with boundary and show that acoustic
measurements with sources and receivers on disjoints sets on the
boundary determine the manifold uniquely assuming that the wave
equation is exactly controllable from the set of sources. The exact
controllability can be characterized in terms of the billiard flow of
the manifold. We will also consider the problem to determine lower
order terms in a wave equation.