Field theoretic renormalization group for a nonlinear diffusion equation
| dc.creator | Antonov, N. V. | |
| dc.creator | Honkonen, Juha | |
| dc.date | 2002-07-02 | |
| dc.date.accessioned | 2026-07-07T12:16:59Z | |
| dc.date.available | 2026-07-07T12:16:59Z | |
| dc.description | The 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.description | 8 pages, 2 figures, RevTeX | |
| dc.identifier | https://arxiv.org/abs/nlin/0207006 | |
| dc.identifier | http://arxiv.org/abs/nlin/0207006 | |
| dc.identifier | Phys.Rev.E66:046105,2002 | |
| dc.identifier | doi:10.1103/PhysRevE.66.046105 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/211978 | |
| dc.subject | Chaotic Dynamics | |
| dc.title | Field theoretic renormalization group for a nonlinear diffusion equation | |
| dc.type | text |