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Renormalizing partial differential equations

  • Partial Differential Equations
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Constructive Physics Results in Field Theory, Statistical Mechanics and Condensed Matter Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 446))

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.

Supported by EC grants SCl-CT91-0695 and CHRX-CT93-0411

Supported by NSF grant DMS-9205296 and EC grant CHRX-CT93-0411

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Authors and Affiliations

  1. UCL, Physique Théorique, B-1348, Louvain-la-Neuve, Belgium

    Jean Bricmont

  2. Department of Mathematics, Helsinki University, 00014, Helsinki, Finland

    Antti Kupiainen

Authors
  1. Jean Bricmont
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  2. Antti Kupiainen
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Vincent Rivasseau

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© 1995 Springer-Verlag

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Bricmont, J., Kupiainen, A. (1995). Renormalizing partial differential equations. In: Rivasseau, V. (eds) Constructive Physics Results in Field Theory, Statistical Mechanics and Condensed Matter Physics. Lecture Notes in Physics, vol 446. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59190-7_23

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  • DOI: https://doi.org/10.1007/3-540-59190-7_23

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  • Print ISBN: 978-3-540-59190-0

  • Online ISBN: 978-3-540-49222-1

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