Reconstruction of the time-dependent source term in a stochastic fractional diffusion equation

Abstract

In this work, an inverse problem in the fractional diffusion equation with random source is considered. The measurements we use are the statistical moments of the realizations of single point observation $ u(x_0,t,\omega). $ We build a representation of the solution $ u $ in the integral sense, then prove some theoretical results like uniqueness and stability. After that, we establish a numerical algorithm to solve the unknowns, where a mollification method is used.

Topics & Concepts