[Dottorcomp] Seminari di Matematica Applicata, 23/04/2024, Jürgen Sprekels

[Stefano Lisini]

Seminari di Matematica Applicata, Dipartimento di Matematica "F. Casorati"
e Istituto del CNR IMATI "E. Magenes" di Pavia.

Martedì 23 aprile 2024, alle ore 15.00 precise, presso l'aula Beltrami del
dipartimento di Matematica,

Jürgen Sprekels (WIAS and HU Berlin)terrà un seminario dal titolo:

Optimality conditions in the sparse optimal control of viscous
Cahn-Hilliard systems.

Il seminario verrà anche trasmesso su zoom al link:

https://zoom.us/j/87518137128?pwd=eHg2eG9QZUdydFJEU1NESWN5a1lPQT09


Abstract.
In this talk, we study the optimal control of a viscous Cahn-Hilliard
system with zero Neumann boundary conditions and logarithmic potential. To
enhance the occurrence of sparsity for locally optimal controls, the cost
functional contains a convex, but nondifferentiable, contribution which is
typically given by an L^1-type norm.  It is demonstrated that for such
control problems with nondifferentiable costs not only first-order
necessary, but also meaningful second-order sufficient optimality
conditions for locally optimal controls can be derived. For the latter,
quite a bit of technical effort is needed, since not only the presence of
the nondifferentiable term but also the so-called “two-norm discrepancy“
have to be overcome. The method used here is based on a clever choice of
the “critical cone“ on which the second derivative of the differentiable
part of the cost functional has to be positive definite. This is a joint
work with P. Colli (U Pavia) and F. Tröltzsch (TU Berlin).


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