Optimal Control Of Two Kinds Of Partial Differential Equations With Conjugate Conditions

Partial differential equation is an important tool to solve mathematical problems and life problems.Optimal control theory is an important independent field in applied mathematics.It also promotes the rapid development of optimization theory and method.However,in real life,many problems that need to be optimized can not be solved by ordinary differential equations,such as epidemic propagation,heat conduction,electromagnetic wave conduction and so on,so it is of great practical significance to study the optimal control problem of partial differential equations.In this paper,we study the optimal control of two classes of partial differential equations with conjugated conditions,and prove the necessary conditions for the existence of optimal control.It is divided into three chapters:The first chapter mainly introduces the historical background and research significance of partial differential equations,expounds the origin and research object of the optimal control problem of partial differential equations,and analyzes the current research status and research results at home and abroad.In the second chapter,we study the optimal control problem for a class of parabolic equations with conjugate conditions.Select the appropriate target function,the existence of optimal control and optimal solution of the system in a given space and necessary condition for existence of the control u are proved.In the third chapter,on the basis of the second order of the parabolic equation,the optimal control problem of a class of pseudo-parabolic equations with common condition is studied.Convert the objective function to find a u to make the optimal control problem exist,that satisfies any of the conditions u(?)are called optimal control,necessary conditions for optimal controls are established by formally differentiating the cost functional with respect to the control.