Renormalization Group and Asymptotics of Solutions of Nonlinear Parabolic Equations

J. Bricmont; A. Kupiainen; G. Lin

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Renormalization Group and Asymptotics of Solutions of Nonlinear Parabolic Equations

J. Bricmont·A. Kupiainen·G. Lin

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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.

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J. Bricmont, A. Kupiainen, G. Lin. 1993-06-21. Renormalization Group and Asymptotics of Solutions of Nonlinear Parabolic Equations. https://arxiv.org/abs/chao-dyn/9306008

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