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Determining the initial distribution in space-fractional diffusion by a negative exponential regularization method. (English) Zbl 1369.65137

Summary: 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 an a posteriori regularization parameter choice rule, the convergence rate estimate are established under a-priori bound assumption for the exact solution. Finally, several numerical examples are proposed to show that the numerical methods are effective.

MSC:

65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
65N20 Numerical methods for ill-posed problems for boundary value problems involving PDEs
35R11 Fractional partial differential equations
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