Bang-Bang Property of Time Optimal Control for a Kind of Microwave Heating Problem

In this paper, the bang–bang property and the existence of the solution for the time optimal control of a specific kind of microwave heating problem are studied. The mathematical model for the time optimal control problem (P) of microwave heating is formulated, in which the governing equations of the controlled system are the weak coupling system of Maxwell equations and the heat equation. Based on a new observability estimate of the heat controlled system, the controllability of the system is derived by proving the null controllability of an equivalent system. The existence of the time optimal control of microwave heating is acquired under some stated assumptions, enabling the bang–bang property of the time optimal control problem (P) to be achieved.