Tuesday, 13 September 2016, 3 p.m. (sharp), Prof. Jürgen Sprekels (WIAS e Humboldt University, Berlino), at the conference room of IMATI-CNR in Pavia, will give a lecture titled:
A NEW IDENTIFICATION PROBLEM: OPTIMIZING THE FRACTIONAL ORDER IN A NONLOCAL EVOLUTION PROBLEM
as part of the Applied Mathematics Seminar (IMATI-CNR e Dipartimento di Matematica, Pavia).
At the end a refreshment will be organized.
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 s-th 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
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