Field theoretic renormalization group for a nonlinear diffusion equation

dc.creatorAntonov, N. V.
dc.creatorHonkonen, Juha
dc.date2002-07-02
dc.date.accessioned2026-07-07T12:16:59Z
dc.date.available2026-07-07T12:16:59Z
dc.descriptionThe paper is an attempt to relate two vast areas of the applicability of the renormalization group (RG): field theoretic models and partial differential equations. It is shown that the Green function of a nonlinear diffusion equation can be viewed as a correlation function in a field-theoretic model with an ultralocal term, concentrated at a spacetime point. This field theory is shown to be multiplicatively renormalizable, so that the RG equations can be derived in a standard fashion, and the RG functions (the $β$ function and anomalous dimensions) can be calculated within a controlled approximation. A direct calculation carried out in the two-loop approximation for the nonlinearity of the form $ϕ^α$, where $α>1$ is not necessarily integer, confirms the validity and self-consistency of the approach. The explicit self-similar solution is obtained for the infrared asymptotic region, with exactly known exponents; its range of validity and relationship to previous treatments are briefly discussed.
dc.description8 pages, 2 figures, RevTeX
dc.identifierhttps://arxiv.org/abs/nlin/0207006
dc.identifierhttp://arxiv.org/abs/nlin/0207006
dc.identifierPhys.Rev.E66:046105,2002
dc.identifierdoi:10.1103/PhysRevE.66.046105
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/211978
dc.subjectChaotic Dynamics
dc.titleField theoretic renormalization group for a nonlinear diffusion equation
dc.typetext

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