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
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Birkhäuser Verlag Basel/Switzerland
About this chapter
Cite this chapter
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
Download citation
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
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)