A Solution of the Heat Equation with a Continuum of Decay Rates

  • Thierry Cazenave
  • Flávio Dickstein
  • Fred B. Weissler
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 63)

Abstract

In this paper, we prove the existence of a solution of the heat equation on \(\mathbb{R}^N \) which decays at different rates along different time sequences going to infinity. In fact, all decay rates \(t^{ - \frac{\sigma } {2}} \) with 0 < σ < N are realized by this solution.

Keywords

heat equation asymptotic behavior decay rate 

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References

  1. [1]
    Cazenave T., Dickstein F. and Weissler F.B. Universal solutions of the heat equation on \(\mathbb{R}^N \), Discrete Contin. Dynam. Systems 9 (2003), 1105–1132.MathSciNetGoogle Scholar
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    Cazenave T., Dickstein F. and Weissler F.B. Multiscale asymptotic behavior of a solution of the heat equation in \(\mathbb{R}^N \), preprint, 2005.Google Scholar
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    Cazenave T., Dickstein F. and Weissler F.B. A solution of the heat equation in \(\mathbb{R}\)with exceptional asymptotic properties, preprint, 2005.Google Scholar
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    Vázquez J.L. and Zuazua E. Complexity of large time behaviour of evolution equations with bounded data, Chinese Ann. Math. Ser. B 23 (2002), 293–310.MathSciNetGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2005

Authors and Affiliations

  • Thierry Cazenave
    • 1
  • Flávio Dickstein
    • 2
  • Fred B. Weissler
    • 3
  1. 1.Laboratoire Jacques-Louis Lions, UMR CNRS 7598 B.C. 187Université Pierre et Marie CurieParis Cedex 05France
  2. 2.Instituto de MatemáticaUniversidade Federal do Rio de JaneiroRio de Janeiro, R.J.Brazil
  3. 3.LAGA UMR CNRS 7539Institut Galilée-Université Paris XIIIVilletaneuseFrance

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