A Mollification Regularization Method for a Fractional-Diffusion Inverse Heat Conduction Problem

Abstract EN

The ill-posed problem of attempting to recover the temperature functions from one measured transient data temperature at some interior point of a one-dimensional semi-infinite conductor whenthe governing linear diffusion equation is of fractional type is discussed.

A simple regularization method based on Dirichlet kernel mollification techniques is introduced.

We also propose a priori and a posteriori parameter choice rules and get the corresponding error estimate between the exact solution and its regularized approximation.

Moreover, a numerical example is provided to verify our theoretical results.