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.
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References
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.
Cazenave T., Dickstein F. and Weissler F.B. Multiscale asymptotic behavior of a solution of the heat equation in \(\mathbb{R}^N \), preprint, 2005.
Cazenave T., Dickstein F. and Weissler F.B. A solution of the heat equation in \(\mathbb{R}\)with exceptional asymptotic properties, preprint, 2005.
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.
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© 2005 Birkhäuser Verlag Basel/Switzerland
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Cazenave, T., Dickstein, F., Weissler, F.B. (2005). A Solution of the Heat Equation with a Continuum of Decay Rates. In: Bandle, C., et al. Elliptic and Parabolic Problems. Progress in Nonlinear Differential Equations and Their Applications, vol 63. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7384-9_15
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DOI: https://doi.org/10.1007/3-7643-7384-9_15
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7249-1
Online ISBN: 978-3-7643-7384-9
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