Evolution equations, invariant surface conditions and functional separation of variables

This paper is devoted to a discussion of the reduction methods for evolution equations based on invariant surface conditions related to functional separation of variables. The relationship of these methods with nonclassical and weak point symmetries is stressed. Applications to diffusion equations with an inhomogeneous reaction term or with saturating dissipation are provided, (C) 2000 Elsevier Science B.V. All rights reserved.