Optimization with Respect to Order in a Fractional Diffusion Model: Analysis, Approximation and Algorithmic Aspects - Antil, Harbir; Otárola, Enrique; Salgado, Abner J. (Journal of scientific computing, 2018)
We consider an identification (inverse) problem, where the state u is governed by a fractional elliptic equation and the unknown variable corresponds to the order s ∈ ( 0 , 1 ) of the underlying operator. We study the existence of an optimal pair ( s ¯ , u ¯ ) and provide sufficient conditions for its local uniqueness. We develop semi-discrete and fully discrete algorithms to approximate the solutions to our identification problem and provide a convergence analysis. We present numerical illustrations that confirm and extend our theory.