A new identification problem: optimizing the fractional order in a nonlocal evolution problem
Prof. Jürgen Sprekels (WIAS and Humboldt University, Berlin, Germany)
Sala Conferenze, IMATI-CNR - Tuesday, September 13, 2016 h.15:00
Abstract. In this lecture, we consider a rather general linear evolution equation of fractional type, namely a diffusion type process in which the diffusion operator is the sth power of a positive definite linear operator having a discrete spectrum of positive eigenvalues. We prove existence, uniqueness and differentiablity properties with respect to the fractional parameter s. These results are used to derive existence as well as first-order necessary and second-order sufficient optimality conditions for a minimization problem, which is inspired by considerations in mathematical biology. In this minimization problem, the fractional parameter s serves as the "control" parameter that needs to be chosen in such a way that a suitable cost functional is minimized.
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