Nonlinear inverse problem of control diffusivity parameter determination for a space-time fractional diffusion equation

摘要

In paper the nonlinear inverse problem of finding a control parameter in a space-time fractional diffusion equation with varying degrees of heterogeneity is investigated. An iterative method for finding an unknown control parameter is proposed. Under the maximal regularity condition respecting input data on the Bessel potential scale, the existence and uniqueness of a solution of such inverse problem are shown. Results are illustrated by examples. An example of numerical simulation of an iterative algorithm is given.