Sparse Controls for the Optimization of Traveling Wave Fronts

Christopher Ryll*, Fredi Tröltzsch and Eduardo Casas

We consider optimal sparse control problems for reaction diffusion equations, like the Schlögl equation in spatial dimension one and two as well as the FitzHugh-Nagumo system in spatial dimension two. Both have in common, that their solutions form pattern of traveling wave fronts or even spiral waves. We derive first-order necessary optimality conditions for the associated control problems as well as sparsity of the controls and present various numerical examples.

Mathematics Subject Classification: 49K20 49M05 35K57

Keywords: optimal control; reaction-diffusion system; sparse control; traveling wave fronts; spiral waves

Minisymposion: Stability, Sensitivity and Error Analysis for Optimal Control Problems