Ph.D. Thesis Viva: Mr. Soumen Senapati: Stability and Uniqueness Results for Hyperbolic and Parabolic Inverse Problems

In this talk, we are going to discuss the following problems.

• Stability for formally over determined problems: We consider lower order perturbations to the usual wave and heat operator which represent some time-evolving properties

of a homogeneous medium. We are interested in stably determining those perturbations by applying initial and boundary source and then measuring the corresponding output on a part of the boundary or at final time. The stability results here are logarithmic in nature.
• Stability for formally determined problems: For the perturbed wave operator, we consider the initial value problems corresponding to plane waves with different time delay or point sources with different activation time. With the final time measurements, we study the stable determination of the unknown coefficients and discuss Lipschitz recovery results
for these formally determined problems.

• A uniqueness result for light ray transform: We present a uniqueness and decompotion result for a symmetric 2 tensor from its line integrals along light rays. More importantly, the light rays here are allowed to vary only in a neighbourhood of a fixed light ray.