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Evolution equations, invariant surface conditions and functional separation of variables. (English) Zbl 0989.35011

Summary: 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.

MSC:

35A25 Other special methods applied to PDEs
35A30 Geometric theory, characteristics, transformations in context of PDEs
35K55 Nonlinear parabolic equations
35R30 Inverse problems for PDEs
58J70 Invariance and symmetry properties for PDEs on manifolds
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