Renormalizing Partial Differential Equations

Details Renormalizing Partial Differential Equations Renormalizing Partial Differential Equations

1994-11-14

arxiv.org/abs/chao-dyn/9411015v1

Nonlinear Sciences

Chaotic Dynamics

34 pages, Latex; bricmont@fyma.ucl.ac.be; ajkupiai@cc.helsinki.fi

Scientific paper

10.1007/3-540-59190-7_23

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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