Renormalization-group and Asymptotics of Solutions of Nonlinear Parabolic Equations

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. In an accompanying paper, [5], the method is applied to systems of equations where some variables are ''slaved,'' such as the complex Ginzburg-Landau equation. (c) 1994 John Wiley & Sons, Inc