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arxiv: chao-dyn/9411015 · v1 · submitted 1994-11-14 · chao-dyn · nlin.CD

Renormalizing Partial Differential Equations

J.Bricmont (UCL , Physique Th\'eorique , B-1348 , Louvain-la-Neuve , Belgium) A.Kupiainen (Helsinki University , Department of Mathematics , Helsinki 00014 , Finland) This is my paper
classification chao-dyn nlin.CD
keywords equationsdifferentialpartialanalysisanomalousapplicationsapplyasymptotics
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In this review paper, we explain how to apply Renormalization Group ideas to the analysis of the long-time asymptotics of solutions of partial differential equations. We illustrate the method on several examples of nonlinear parabolic equations. We discuss many applications, including the stability of profiles and fronts in the Ginzburg-Landau equation, anomalous scaling laws in reaction-diffusion equations, and the shape of a solution near a blow-up point.

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