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Differential constraints and exact solutions of nonlinear diffusion equations. (English) Zbl 1039.35054

Summary: The differential constraints are applied to obtain explicit solutions of nonlinear diffusion equations. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the determining equations used in the search for classical Lie symmetries.

MSC:

35K57 Reaction-diffusion equations
35A30 Geometric theory, characteristics, transformations in context of PDEs
35C05 Solutions to PDEs in closed form
34G20 Nonlinear differential equations in abstract spaces
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