Symmetries and group-invariant solutions to a new family of higher order nonlinear degenerate parabolic equations
WANG Lizhen, HUANG Qing, KANG Xiaoyu, ZUO Suli
(Department of Mathematics, Northwest University, Xi′an 710127, Shaanxi, China)
Abstract:
A type of higher order nonlinear degenerate parabolic equations is investigated. Using the method of Lie symmetry, the finite dimensional symmetries generated by four vector fields and the one-dimensional optimal system formed by seven nonequivalent sub-algebras are constructed. When p=2 and n=1, for Newton fluid, two types of group invariant solutions are obtained and when p=3 and n=1, for ‘power-law’ liquids, three types of group invariant solutions are derived. It is shown that there exist blow up group invariant solutions in both cases.
KeyWords:
nonlinear degenerate parabolic equation; Lie symmetry group; optimal system; group invariant solution
