Conditional Lie-Bäcklund symmetries to inhomogeneous nonlinear diffusion equations

In this paper, conditional Lie-Bäcklund symmetry method is used to classify a class of inhomogeneous nonlinear diffusion equations ut=e-qxepxw(u)uxx. Equations admitted conditional Lie-Bäcklund symmetries can be either solved exactly or reduced to finite-dimensional dynamical systems. A number of concrete examples defined on the exponential and trigonometric invariant subspaces are considered to illustrate this method.