Exact self-similar solution of a certain equation of non-linear diffusion with dissipationстатья
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Аннотация:Using the renormalization-group method, an exact solution of the equation of non-linear diffusion with dissipation of the Cahn-Hilliard type is obtained. When finding an admissible form of the self-similar solution, only dimensionality arguments and the property of renormalization invariance are used. The form of the initial and boundary conditions, consistent with the non-linear equation cannot be given in advance, but is found from the solution of the renormalization-group equations. (C) 2015 Elsevier Ltd. All rights reserved.