A class of nonlinear reaction-diffusion-convection equations describing various processes in physics, biology, chemistry etc. is under study in the case of time and two space variables. The group of equivalence transformations is constructed, which is applied for deriving a Lie symmetry classification for the class of such equations by the well-known algorithm. It is proved that the algorithm leads to 32 reaction-diffusion-convection equations admitting nontrivial Lie symmetries. Furthermore a set of form-preserving transformations for this class is constructed in order to reduce this number of the equations and obtain a complete Lie symmetry classification. As a result, the so called canonical list of all inequivalent equations admitting nontrivial Lie symmetry (up to any point transformations) and their Lie symmetries are derived. The list consists of 22 equations and it is shown that any other reaction-diffusion-convection equation admitting a nontrivial Lie symmetry is reducible to one of these 22 equations. As a nontrivial example, the symmetries derived are applied for the reduction and finding exact solutions in the case of the porous-Fisher type equation with the Burgers term.

在时间和两个空间变量的情况下，正在研究一类描述物理，生物学，化学等各个过程的非线性反应扩散对流方程。构造了等价变换的组，该变换用于通过众所周知的算法推导此类方程组的李对称性分类。实践证明，该算法导致了32个具有非平凡Lie对称性的反应扩散对流方程。此外，为此类构造了一组保形变换，以减少方程的数量并获得完整的李对称性分类。结果，得出了所有允许不平凡的李对称性（直到任何点变换）的不等式的所谓规范列表及其李对称性。该列表由22个方程组成，并且显示出任何其他允许非平凡的Lie对称性的反应扩散对流方程都可归纳为这22个方程之一。作为一个非平凡的例子，在具有Burgers项的多孔Fisher型方程的情况下，导出的对称性用于简化和找到精确解。