92-43 Bricmont J., Kupiainen A., Lin G.

Renormalization Group and asymptotics of solutions of nonlinear parabolic equations (65K, LATEX) Mar 5, 92

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Abstract. 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 , the method is applied to systems of equations where some variables are "slaved", such as the complex Ginzburg-Landau equation.

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