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Asymptotics of Partial Differential Equations and the Renormalisation Group

  • Nigel Goldenfeld
  • Olivier Martin
  • Y. Oono
Part of the NATO ASI Series book series (NSSB, volume 284)

Abstract

It is well-known that the asymptotics of partial differential equations (PDEs) may often be found from consideration of similarity solutions. In the examples usually encountered, the combinations of variables making up the similarity variables may be deduced using dimensional analysis; typically, the similarity variables are products of variables raised to rational fraction powers. It is not so widely appreciated, however, that there is a large class of problems where the similarity variables cannot be deduced from dimensional analysis. As Barenblatt has emphasized, such problems are neither rare nor pathological, but occur in many situations of physical interest, for example, in continuum mechanics.1

Keywords

Renormalisation Group Anomalous Dimension Dimensional Analysis Perturbation Expansion Steady State Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • Nigel Goldenfeld
    • 1
  • Olivier Martin
    • 2
  • Y. Oono
    • 1
  1. 1.Department of PhysicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.Department of Physics, City CollegeCUNYNew YorkUSA

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