Some Exact Solutions Of Geometrical Flows And Generalized Tricomi Equation

Geometrical flows are related to Poinc?are's conjecture and quantum theory.The generalized Tricomi equations are linear partial equations related to aerodynamic.In this dissertation,some exact solutions of geometrical flows and the generalized Tricomi equations are given.The behaviors of some solutions are also described.Two problems are considered as follows:(1)In the sense of change of variables,separable solutions to the geometrical flows are constructed by invariant subspace method and ans¨atz-based method.Product separable solutions and generalized functional separable solutions are included.The behavior to these solutions are described;(2)Lie symmetry group,the corresponding reduced equations and groupinvariant solutions of the generalized Tricomi equations for different cases are presented.