Elliptic and Parabolic Problems

Volume 63 of the series Progress in Nonlinear Differential Equations and Their Applications pp 135-138

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

  • Thierry CazenaveAffiliated withLaboratoire Jacques-Louis Lions, UMR CNRS 7598 B.C. 187, Université Pierre et Marie Curie
  • , Flávio DicksteinAffiliated withInstituto de Matemática, Universidade Federal do Rio de Janeiro
  • , Fred B. WeisslerAffiliated withLAGA UMR CNRS 7539, Institut Galilée-Université Paris XIII

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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.


heat equation asymptotic behavior decay rate