Determining the initial distribution in space-fractional diffusion by a negative exponential regularization method.

In this paper, we consider the backward problem for diffusion equation with space fractional Laplacian, i.e. determining the initial distribution from the final value measurement data. In order to overcome the ill-posedness of the backward problem, we present a so-called negative exponential regularization method to deal with it. Based on the conditional stability estimate and ana posterioriregularization parameter choice rule, the convergence rate estimate are established undera-prioribound assumption for the exact solution. Finally, several numerical examples are proposed to show that the numerical methods are effective. [ABSTRACT FROM PUBLISHER]