Relaxation and optimisation of a phase-field control system with hysteresis

摘要

The present paper is concerned with a nonlinear partial differential control system arising in phase transition modelling. The control constraint is given by a state-dependent nonconvex-valued multi-valued mapping. We study the problem of minimisation of a given integral cost functional over solutions to the above system. The cost integrand is nonconvex in the control variable. Relaxation results of Bogolyubov-type are obtained for this problem.