Determining the random source and initial value simultaneously in stochastic fractional diffusion equations
Determining the random source and initial value simultaneously in stochastic fractional diffusion equations
In this paper, we investigate the inverse problem of recovering unknown random source and initial value simultaneously from statistical measurement data in a time-fractional stochastic diffusion equation. Based on the eigenfunction expansions, we first establish the statistical moments estimate for the solution of direct problem. Then the conditional stability for …