关键词: (2+1)维拟线性抛物方程； 不变子空间； 泛函分离变量； 精确解

Abstract:

Utilizing conditional Lie-Bcklund symmetry associated with invariable subspace theory, we studied three types of generalized functional separation variable solutions for (2+1)dimensional quasilinear parabolic equation, that is, generalized functional polynomial type solution, generalized functional trigonometric function type solution and generalized functional exponent type solution. As a result, a complete classification of the quasilinear equation was obtained. At the same time, we obtained the dynamic system  satisfied  by the unknown function among the exact solution.

Key words: (2+1)dimensional quasilinear parabolic equation, invariant subspace, functional separation variable, exact solution