Insensitizing Controls And Inverse Problems For Coupled Linear Complex Ginzburg-landau Systems

This dissertation is devoted to a study of insensitizing controls and a class of inverse problems for coupled linear complex Ginzburg-Landau systems.The Carleman estimates method is adopted.The action of an insensitizing control is to guarantee that some energy of a system almost does not vary,when initial measurements have small errors,that is,this control is used to remove sensitivity of the system with respect to perturbances.In order to establish the existence of insensitizing controls for coupled linear complex Ginzburg-Landau systems,it is transformed into a controllability problem of a coupled system governed by two forward and backward complex Ginzburg-Landau equations but only through one control force.The known insensitizing control results are mainly established for single evolution equations.In a known result on insensitivity for coupled real parabolic systems,the energy is only related to one solution component.This dissertation is devoted to a class of coupled complex parabolic systems and energy depends on all solution components.By the fixed point technique,the results in this dissertation can be generalized to general nonlinear complex-valued coupled systems.On the other hand,a class of inverse time problems for coupled linear complex GinzburgLandau systems are established.When systems are constant,an equivalent characterization on coupled coefficients for the observability inequality is given.Also,the backward uniqueness and a class of conditional stability results are derived for coupled systems.