Group classification for nonlinear filtration problem

摘要

In this paper we investigate the group classification for all possible prosity functions K(t,x,y,h) for the filtration problem modeled by H. Rouse (Engineering hydraulic, in: Proceedings of the Fourth Hydraulic Conference, Institute of Hydraulic Research, 12–15 June, 1949, pp. 383–385). Moreover, some classes of invariant solutions are obtained.