Date:

Monday, November 18, 2002

Speaker:

Frederico C. Furtado

Affiliation:

Department of Mahematics, University of Wyoming

e-mail:

furtado@uwyo.edu

Title:

Numerical renormalization-group approach to self-similar dynamics

Abstract:

We present a systematic computational approach to the study of long-time self-similar dynamics. This approach is based on the renormalization group (RG) for partial differential equations, and is able to treat both first and second kind self-similar dynamics, in Barenblatt's classification. We show that successive iterations of a discrete RG transformation in space and time drive the system towards a fixed point, which corresponds to a self-similar dynamics. We illustrate the method on several examples of nonlinear parabolic equations displaying anomalous scaling laws, including the modified porous medium equation---which describes, e.g., the problem of gravity-driven ground water---and Barenblatt's equation---which describes the flow of an elastic fluid in an elasto-plastic porous medium.