Inverse problems for fractional parabolic equations with power type nonlinearities

Abstract: I will first introduce classical and fractional Calderón problems. Then I will focus on two inverse problems for fractional parabolic equations with power type nonlinearities. Both can be viewed as nonlinear parabolic variants of the fractional Calderón problem. The goal is to determine nonlinearities/coefficients in fractional equations from exterior partial measurements of the Dirichlet-to-Neumann map. The approach relies on the unique continuation property of the fractional operator as well as techniques relating nonlinear problems to linear ones.

Mathematics

Audience: researchers in the topic

International Zoom Inverse Problems Seminar, UC Irvine