Abstract
We present a renormalization-group (RG) approach to the nonlinear diffusion process u=D u, with D=1/2 for u>0 and D=(1+ε)/2 for u<0, which describes the pressure during the filtration of an elastic fluid in an elastoplastic porous medium. Our approach recovers Barenblatt’s long-time result that, for a localized initial pressure distribution, u(x,t)∼f(x/ √t, ε), where f is a scaling function and α=ε(2πe+O() is an anomalous dimension, which we compute perturbatively using the RG. This is the first application of the RG to a nonlinear partial differential equation in the absence of noise.
- Received 22 January 1990
DOI:https://doi.org/10.1103/PhysRevLett.64.1361
©1990 American Physical Society