Properties For Some Quenching Ordinary Differential Equations And Their Quenching Time Optimal Control Problems

This thesis studies some quenching ordinary differential equations and their quenching time optimal control problems.The full text is divided into three sections. The first section outlines the background. Next, we study the properties of two types of ordinary differential equations. We get the existence, the invariant property of solutions and the quenching rate estimate. In section3, we prove the existence of quenching time optimal controls according to the results obtained in section2.