Institut für Mathematik
Optimal and Feedback Control of Some Reaction-Diﬀusion Equations
The optimal control of some systems of nonlinear reaction-diﬀusion equations is considered including the Nagumo and FitzHugh-Nagumo equations. These equations are known to develop traveling wave fronts, spiral waves or scroll rings as solutions. Well-posedness of the system, diﬀerentiability of the control-to-state mapping, and optimality conditions of ﬁrst order are brieﬂy sketched. In particular, the case of sparse optimal control is addressed. Moreover, the optimization of time-delays in local and nonlocal Pyragas type feedback control up to the control by measures is discussed. Various numerical examples illustrate the great diversity of geometrical patterns and their control.
Prof. Dr. Fredi Tröltzsch (TU Berlin)
Senka Haznadar (senka [dot] haznadar [at] aau [dot] at)