Translator Disclaimer
2000 The determination of caloric morphisms on Euclidean domains
Katsunori Shimomura
Nagoya Math. J. 158: 133-166 (2000).

Abstract

Let $D$ be a domain in ${\Bbb R}^{m+1}$ and $E$ be a domain in ${\Bbb R}^{n+1}$. A pair of a smooth mapping $f:D \to E$ and a smooth positive function $\varphi$ on $D$ is called a caloric morphism if $\varphi\cdot u \circ f$ is a solution of the heat equation in $D$ whenever $u$ is a solution of the heat equation in $E$. We give the characterization of caloric morphisms, and then give the determination of caloric morphisms. In the case of $m<n$, there are no caloric morphisms. In the case of $m=n$, caloric morphisms are generated by the dilation, the rotation, the translation and the Appell transformation. In the case of $m>n$, under some assumption on $f$, every caloric morphism is obtained by composing a projection with a direct sum of caloric morphisms of ${\Bbb R}^{n+1}$.

Citation

Download Citation

Katsunori Shimomura. "The determination of caloric morphisms on Euclidean domains." Nagoya Math. J. 158 133 - 166, 2000.

Information

Published: 2000
First available in Project Euclid: 27 April 2005

zbMATH: 0970.31006
MathSciNet: MR1766569

Subjects:
Primary: 35K05
Secondary: 35A30

Rights: Copyright © 2000 Editorial Board, Nagoya Mathematical Journal

JOURNAL ARTICLE
34 PAGES


SHARE
Vol.158 • 2000
Back to Top