Nonlinear Reaction Diffusion Equations Generalized Conditional Symmetries And Its Exact Solution

The nonlinear phenomena widely appear in almost all the fields such as physics, biology, nature, chemistry, society, economy and so on. With the development of science, more attention to the nonlinear phenomena that reflects natural phenomena are taken, then the researches on the nonlinear systems are taking more and more progress. The problem of solving the partial differential equation is becoming one of the important and main researches.Symmetry methods play a key role in the researches of exact solutions of partial differential equation. Lie group approach is an effective method in the study of exact solutions. But in fact, many partial differential equations don't allow rich enough symmetry groups. So as the generalization of Lie group approaches, many other methods are obtained, such as: conditional symmetry method, generalized symmetry method, generalized conditional symmetry method, etal.Nonlinear reaction equationes based on physics are studied with generalized conditional symmetry method. As a result, some exact solutions are given.In chapter 1, some methods used in the research of partial differential equations are introduced, especially the generalized conditional symmetry method.In chapter 2, nonlinear reaction diffusion convection equationis studied with the method of generalized conditional symmetry method.In chapter 3, nonlinear diffusion equationis studied with the method of generalized conditional symmetry method.