BibTeX
@MISC{94renormalizingpartial,
author = {},
title = {Renormalizing Partial Differential Equations},
year = {1994}
}
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Abstract
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. 1 Introduction. The development of a qualitative theory of infinite dimensional dynamical systems is a major scientific challenge. Such systems are expressed through (nonlinear) partial differential equations, and we shall concentrate on equations of the form ut = ∆u + F(u, ∇u, ∇∇u). (1)
Keyphrases
partial differential equation blow-up point long-time asymptotics form ut many application several example infinite dimensional dynamical system ginzburg-landau equation renormalization group idea nonlinear parabolic equation reaction-diffusion equation major scientific challenge qualitative theory
