Invariant subspaces and conditional Lie-Baeicklund symmetries of inhomogeneous nonlinear diffusion equations

The inhomogeneous nonlinear diffusion equation is studied by invariant subspace and condi- tional Lie=Bgcklund symmetry methods. It is shown that the equations admit a class of invariant subspaces governed by the nonlinear ordinary differential equations, which is equivalent to a kind of higher=order conditional Lie-B~icklund symmetries of the equations. As a consequence, a number of new solutions to the inhomogeneous nonlinear diffusion equations are constructed explicitly or reduced to solving finite-dimensional dynamical sys- tems.