Long time heat diffusion on homogeneous trees
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- by Guia Medolla and Alberto G. Setti PDF
- Proc. Amer. Math. Soc. 128 (2000), 1733-1742 Request permission
Abstract:
Let ${\mathfrak {X}}$ be a homogeneous tree of degree $q+1$, $q\geq 2$, ${\mathcal {L}}$ the Laplace operator of ${\mathfrak {X}}$ and $h_{t}(x)$ the fundamental solution of the heat equation $(\partial _{t} +{\mathcal {L}}) u=0$ on $\mathfrak {X}$. We show that the heat kernel $h_{t}(x)$ is asymptotically concentrated in an annulus moving to infinity with finite speed $R_{1}=(q-1)/(q+1)$. Asymptotic concentration of heat in the $L^{p}$ norm is also investigated.References
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Additional Information
- Guia Medolla
- Affiliation: Dipartimento di Matematica, Politecnico di Milano, via Bonardi 9, I-20133 Milano, Italy
- Address at time of publication: I.T.I.S Hensemberger, via Berchet, I-20052 Monza, MI, Italy
- Email: guimed@iol.it
- Alberto G. Setti
- Affiliation: Dipartimento di Scienze Chimiche Fisiche e Matematiche, Università dell’Insubria - Polo di Como, via Lucini 3, I-22100 Como, Italy
- MR Author ID: 289546
- Email: setti@fis.unico.it
- Received by editor(s): July 14, 1998
- Published electronically: November 23, 1999
- Additional Notes: The first author acknowledges financial support through a post-doctoral fellowship at the Politecnico di Milano.
- Communicated by: Christopher D. Sogge
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 1733-1742
- MSC (2000): Primary 43A85, 35K05; Secondary 39A12
- DOI: https://doi.org/10.1090/S0002-9939-99-05536-7
- MathSciNet review: 1694874