TY - JOUR

T1 - Field-theoretic renormalization group for a nonlinear diffusion equation

AU - Antonov, N. V.

AU - Honkonen, Juha

PY - 2002/10/10

Y1 - 2002/10/10

N2 - This 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 space-time 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 [formula presented] 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 [formula presented] where [formula presented] 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.

AB - This 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 space-time 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 [formula presented] 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 [formula presented] where [formula presented] 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.

UR - http://www.scopus.com/inward/record.url?scp=85036407686&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.66.046105

DO - 10.1103/PhysRevE.66.046105

M3 - Article

AN - SCOPUS:85036407686

VL - 66

SP - 7

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 4

ER -