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Renormalization Group and Nonlinear PDE’s

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Quantum and Non-Commutative Analysis

Part of the book series: Mathematical Physics Studies ((MPST,volume 16))

Abstract

Renormalization Group was originally developed for the understanding of Critical Phenomena and continuum limit in Quantum Field Theory. We show how similair ideas turn out to be useful in the study of long time asymptotics of solutions of parabolic nonlinear or random Partial Differential Equations. We show how universality, i.e. independence of the asymptotics on initial data and the equation, emerges naturally. Concrete problems discussed include patterns and moving fronts in Ginzburg Landau equation and diffusion in random environment.

Supported by EC Grant SC1-CT91-0695.

Supported by NSF Grant DMS-8903041.

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Author information

Authors and Affiliations

  1. Physique Théorique, UCL, 2, ch. du cyclotron, B-1348, Louvain-la-Neuve, Belgium

    J. Bricmont

  2. Mathematics Department, University of Helsinki, Hallituskatu 15, 00100, Helsinki, Finland

    A. Kupiainen

Authors
  1. J. Bricmont
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  2. A. Kupiainen
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Editor information

Editors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, 606-01, Sakyo-ku, Kyoto, Japan

    Huzihiro Araki

  2. Department of Mathematics and Information, College of Liberal Arts, Kyoto University, Sakyo-ku, Yoshida Kyoto 606, Japan

    Keiichi R. Ito

  3. Department of Mathematics Faculty of Science, Hokkaido University, Sapporo 060, Japan

    Akitaka Kishimoto

  4. Research Institute for Mathematical Sciences, Kyoto University, 606-01, Kyoto, Japan

    Izumi Ojima

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© 1993 Springer Science+Business Media Dordrecht

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Bricmont, J., Kupiainen, A. (1993). Renormalization Group and Nonlinear PDE’s. In: Araki, H., Ito, K.R., Kishimoto, A., Ojima, I. (eds) Quantum and Non-Commutative Analysis. Mathematical Physics Studies, vol 16. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2823-2_8

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  • DOI: https://doi.org/10.1007/978-94-017-2823-2_8

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4334-4

  • Online ISBN: 978-94-017-2823-2

  • eBook Packages: Springer Book Archive

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