Renormalization Group and Asymptotics of Solutions of Nonlinear Parabolic Equations

Details Renormalization Group and Asymptotics of Solutions of Nonlinear Parabolic Equations Renormalization Group and Asymptotics of Solutions of Nonlinear Parabolic Equations

1993-06-21

arxiv.org/abs/chao-dyn/9306008v1

Nonlinear Sciences

Chaotic Dynamics

29 pages

Scientific paper

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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