Dipartimento di Matematica ''F. Casorati''

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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 - Martedì 13 Settembre 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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Dipartimento di Matematica ''F. Casorati''

Università degli Studi di Pavia - Via Ferrata, 5 - 27100 Pavia
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