Renormalization Group and Asymptotics of Solutions of Nonlinear Parabolic Equations

Bricmont, J.; Kupiainen, A.; Lin, G.

Renormalization Group and Asymptotics of Solutions of Nonlinear Parabolic Equations

Authors

Bricmont, J.

Kupiainen, A.

Lin, G.

Description

We present a general method for studying long time asymptotics of nonlinear parabolic partial differential equations. The method does not rely on a priori estimates such as the maximum principle. It applies to systems of coupled equations, to boundary conditions at infinity creating a front, and to higher (possibly fractional) differential linear terms. We present in detail the analysis for nonlinear diffusion-type equations with initial data falling off at infinity and also for data interpolating between two different stationary solutions at infinity.
29 pages