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Geometric properties coded in the long-time asymptotics for the heat equation on $Z^n$

Author: Debe Bednarchak
Journal: Proc. Amer. Math. Soc. 131 (2003), 2261-2269
MSC (2000): Primary 58J35, 58J37
Published electronically: October 24, 2002
MathSciNet review: 1963776
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Abstract: This paper investigates connections between the long-time asymptotics of heat distribution on a body $\Omega$ in $Z^n$, and various geometric properties of $\Omega$, starting from an initially constant heat distribution supported on $\Omega$. We use combinatorial and differential geometric methods. We begin the paper with a result in $R^n$.

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Additional Information

Debe Bednarchak
Affiliation: Department of Mathematics, Long Island University, 1 University Plaza, Brooklyn, New York 11201–8423

Received by editor(s): July 12, 2001
Received by editor(s) in revised form: February 20, 2002
Published electronically: October 24, 2002
Additional Notes: The author was partially supported by the Faculty Scholarship and Development Committee of Long Island University
Communicated by: Jozef Dodziuk
Article copyright: © Copyright 2002 American Mathematical Society