Theoretical and Numerical Research of Control Theory and Identification Problems for nonlinear parabolic and Hyperbolic Distributed parameter System

点击翻译按钮获取中文摘要

According to the research plan, the head investigator studied the optimal control problems and the identification problems for distributed parameter systems described by nonlinear first and second order evolution equations, and studied their numerical analysis based on the finite element method. In the variational framework due to Lions, we have constructed the general theory of optimal control and identification problems for the systems with the help of Drs Ha, Elgamal, Vanualailai and Wang. The general theory can cover a wide class of nonlinear distributed parameter systems such as single sine-Gordon equations and others. Based on the theory and the method we have started to study the more physically important equations such as Cahn-Hilliard equations, Hopfield-type neural network equations, coupled sine-Gordon equation, nonlinear beam equations and Klein-Gordon equations. We can not apply directly our general theory these equations because of the hard nonlinearities of equations. These equations have own proper nonlinear structures and the special analysis of solutions is needed. In order to solve the problems we are required to have the delicate and proper estimates of solutions. Under the conscious of problems, we have succeeded in obtaining the fundamental results of problems for the above equations. Further the head investigator studied the stabilizability and pole assignability for the linear retarded distributed parameter systems of parabolic types. The researches of other investigators are as follows. The investigator Nambu studied the algbraic aspect of stabilization problems for linear parabolic systems. The investigator Tabata proposed and ivestigated new model equations for sociodynamics. The investigator Naito studied nonlinear elliptic equations and established new conditions for the existence and nonexistence of positive radial solutions. The results of the all investigators were published in the journals given below.