Minimal Time Impulse Control Problem of Semilinear Heat Equation

Abstract

The paper is concerned with a kind of minimal time impulse control problem for a semilinear heat equation. We study the existence of optimal controls of this problem, establish a nontrivial Pontryagin’s maximum principle for this problem and then derive the bang–bang property of optimal controls. Based on the existence and the bang–bang property of optimal controls, we discuss the equivalence of the minimal time impulse control problem and its corresponding minimal norm impulse control problem.