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Symmetry reductions and exact solutions of the affine heat equation. (English) Zbl 1149.35306

Summary: Lie symmetry group method is applied to study the affine heat equation for surface. Its symmetry groups and corresponding optimal systems are determined, and group-invariant solutions associated to the symmetries are obtained and classified.

MSC:

35A30 Geometric theory, characteristics, transformations in context of PDEs
58J70 Invariance and symmetry properties for PDEs on manifolds
35C05 Solutions to PDEs in closed form
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