SOME INVERSE PROBLEMS IN HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS

Abstract: In this talk, we will focus on three inverse problems in hyperbolic partial differential equations.

In the first part, we consider the inverse problem of determining time-dependent vector and scalar potentials appearing in the wave equation in space dimension n ≥ 3 from information about the solution on a suitable subset of the boundary cylinder.

In the second part, we consider an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension n ≥ 3. We study the unique determination of quadratic non-linearity appearing in the wave equation from measurements of the solution at the boundary of the spacial domain over finite time interval.

In the third part, we address the inverse problem of determining the density coefficient of a medium by probing it with an external point source and by measuring the responses at a single point (different from the source point) for a certain period of time.

The first part of the talk is joint work with Venky Krishnan, and the second part is done jointly with Gen Nakamura