The Optimal Control Problem For A Parabolic Partial Differential Equation With Blowup Property

This paper studies the optimal control problem for a parabolic partial differential equation with blowup property.In practical applications,people often encounter control problems of control systems governed by partial differential equations with blowup properties.At present,the results of studying the control theory of differential equations with blowup properties are rare.In this paper,the existence and necessary conditions of the optimal control problem for a class of parabolic partial differential equations with blowup properties are obtained by estimating the uniform blowup rate of solutions for inhomogeneous terms by using the method of energy uniform estimation in relevant literatures.