Parameter Identification Problem Of Parabolic Equation

In this paper, we mainly study several methods which can be classified into deterministicmethods and undeterministic methods for the solution of the inverse heat conduction problem.several deterministic methods are introduced for the solution of linear inverse problem andnonlinear problem. In the second chapter we study the methods for the solution of linearinverse problem which are known as two kinds of classical regularization: Tikhonovregularization method and the Landweber regularization method. We compare the twoclassical method. In the third chapter, we focus on discussing some attempts to eliminate illposednessin the nonlinear inverse problem:Parameter regularization method an a example isgiven for the solution of two-dimensional nonlinear inverse problem.In chapter 4 we study theundeterministic methods: Bayes method. In the last chapter we analysis the dialecticalrelationship between forward problem and inverse problem from the viewpoint ofEpistemology and Mathematical Modeling and elaborate the importance of the study ofinverse problem.We shows the extensive of the application of inverse problem and analysisthe philosophy of inverse problem. At last, we analysis the dialectical relationship betweenthe traditional regularization and bayesian method.