2017.05.26, Lecture: An inverse source problem for (time-fractional) diffusion equations

Title:An inverse source problem for (time-fractional) diffusion equations
Abstract:In this talk, we consider the reconstruction of (t) in the (time-fractional) diffusion equation by the observation at a single point x0. We are mainly concerned with the situation of x0 ̸∈ supp g, which is practically important but has not been well investigated in literature. Assuming the finite sign changes of  and an extra observation interval, we establish the multiple logarithmic stability for the problem based on a reverse convolution inequality and a lower estimate for positive solutions. Meanwhile, we develop a fixed point iteration for the numerical reconstruction and prove its convergence. The performance of the proposed method is illustrated by several numerical examples. This is a joint work with Mr. Zhidong Zhang (Texas A&M University).