# Dr. Lauri Oksanen

# Dr. Lauri Oksanen

My research interests include inverse problems for hyperbolic partial differential equations and their relations to geometry. A particular example is the acoustic inverse source problem that is a part ofphotoacoustic tomography.

# Dr Lauri Oksanen

## Research Topics

My research interests include inverse problems for hyperbolic partial differential equations and their relations to geometry.

An example is the following inverse boundary value problem: Given Dirichlet and Neumann traces of a class of solutions to a wave equation on a Riemannian manifold, determine the Riemannian manifold. This is an abstract version of a problem that arises for example in Seismic Imaging and in Ultrasound Tomography.

Another example is the following inverse source problem: Given Dirichlet and Neumann traces of a single solution to a wave equation with known coefficients, determine the corresponding initial data. This problem arises for example in Photoacoustic Tomography and in Control Theory.