Optimal control of anisotropic Allen-Cahn equations

This paper aims at solving an optimal control problem governed by anisotropic Allen-Cahn equation numerically. Therefor we first prove the Frechet differentiability of in time discretized parabolic under certain assumptions on involved quasilinearity and formulate order necessary conditions. As a next step, since anisotropies are general not smooth enough, convergence behavior controls is studied for sequence (smooth) approximations former quasilinear term. In addition simultaneous limit approximation step size considered. For class covering large variety introduce regularization show previously formulated requirements. Finally, trust region Newton solver applied to various configurations, numerical evidence mesh independent with respect presented.