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ALOP- Colloquium with Prof. Fredi Troeltzsch
February 6 / 12:00
Optimal and Feedback Control of some Reaction-Diffusion Equations
The optimal control of some systems of nonlinear reaction-diffusion equations is considered including several important equations of mathematical physics. In particular, equations are covered that develop traveling wave fronts, spiral waves, scroll rings, or propagating spot solutions. Well-posedness of the system, differentiability of the control-to-state mapping, and optimality conditions of first and second order are briefly sketched. In particular, the case of sparse optimal control is addressed. A novel application of pointwise state constraints is presented that prevent a propagating spot from hitting the boundary of the spatial domain. Finally, the optimization of time-delays in local and nonlocal Pyragas type feedback control is discussed. Various numerical examples illustrate a great diversity of geometrical patterns and their control.
The presentation will take place in E51.
Please join us for coffee at 11:45 in E51.