Conditions Of Symmetric Diffusion Equation And Its Exact Solution

The nonlinear phenomena widely appear in almost all the scientific fields such as physics, chemistry, biology, society, economy and so on. With the development of science, researches on the nonlinear systems are making more and more progress. As a result, to deal with the nonlinear equations that describe the nonlinear systems becomes one of the main and hot topics for the researchers.It is well known that the conditional symmetry method is an efficient way and play an important role to study the exact solution of nonlinear partial differential equation(PDE). For the nonlinear PDE, there also have many method to obtain exact solutions, such as the Lie symmetry, direct method, anstaze approach, geometric method, generalized condition symmetry, formal variable separation approach and so on. In this article,we utilize the conditional symmetry method to study nonlinear diffusion equation based on physics.We obtain some interesting exact solutions by utilizing conditional symmetry method to study nonlinear PDE (1.35)In the chapter 1, we introduce some methods to study the exact solution of nonlinear partial differential equations.In the chapter 2, we utilize the conditional symmetry method to study nonlinear diffusion equation (1.35). A complete classification of the functional forms of the reaction coefficients and source terms is presented when the equation admits the conditional symmetry reduction.In the chapter 3,we reduce PDE (1.35),and obtain some exact solutions.