NUMERICAL SOLUTION OF THE INVERSE PROBLEM FOR THE DIFFUSION EQUATION UNDER SPHERICAL SYMMETRY

摘要

We consider an initial-boundary-value problem for the diffusion equation with spherical symmetry and an unknown initial condition. Additional information to determine the unknown initial condition is provided by the external volume potential whose density is a Laplace operator evaluated on the solution of the initial-boundary-value problem. A numerical method is proposed for the corresponding inverse problem. Its efficiency is assessed by a computer experiment.