Quenching Time Optimal Control for Some Ordinary Differential Equations

Abstract

This paper concerns time optimal control problems of three different ordinary differential equations in ${ℝ}^2$. Corresponding to certain initial data and controls, the solutions of the systems quench at finite time. The goal to control the systems is to minimize the quenching time. The purpose of this study is to obtain the existence and the Pontryagin maximum principle of optimal controls. The methods used in this paper adapt to more general and complex ordinary differential control systems with quenching property. We also wish that our results could be extended to the same issue for parabolic equations.