RESEARCH OF OPTIMAL CONTROL AND PARAMETER IDENTIFICATION PROBLEMS FOR NONLINEAR EVOLUTION EQUATIONS

基于泛函分析的方法，研究者将非线性偏微分方程表述为抽象空间中的发展方程。他用变分法和半群理论解决了相关的最优控制、参数辨识和镇定问题。作为应用的结果偏微分方程，他研究了以下五种类型的方程。(1)一阶非线性发展方程(2)非线性波动方程(3)二阶沃尔泰拉型发展方程。(4)具有非局部项的非线性振动方程。(5)耦合对流扩散方程

Based on the method of functional analysis, the investigator has formulated nonlinear partial differential equations as evolution equations in abstract spaces. He has solved the related optimal control, parameter identification and stabilization problems by using the method of variation and the semi-group theory. As applications of the results to partial differential equations, he has studied the following five types of equations.(1) First order nonlinear evolution equations. (2) Nonlinear wave equations.(3) Second order evolution equations of Volterra type.(4) Nonlinear equations of vibration with nonlocal terms.(5) Coupled advection-diffusion equations.