Optimal control of transport-reaction system with time varying spatial domain

This paper deals with the optimal control of multi-dynamics process described by the rigid body dynamics equation and time-varying parabolic PDE. The optimal control is realized for the crystal growth process described by the underlying dynamics of the transport-reaction process given by the parabolic partial differential equations (PDEs) with the time varying spatial domain that is coupled with the rigid body dynamics representing the pulling of the pure crystal out of melt. The underlying transport-reaction system is developed from the first principles and the associated dynamics is analyzed in the appropriate functional state space setting. The complete description of the evolutionary parabolic domain time varying PDE is provided in the operator form and exploited within the optimal control setting, together with the optimal control of crystal pulling out of melt. Numerical simulations demonstrate a realization of optimal control law and its effects on both the temperature profile in the crystal with the time varying domain and crystal domain time evolution.