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July/August 2009 Hot spots for the heat equation with a rapidly decaying negative potential
K. Ishige, Y. Kabeya
Adv. Differential Equations 14(7/8): 643-662 (July/August 2009).

Abstract

We consider the Cauchy problem of the heat equation with a radially symmetric, negative potential $-V$ which behaves like $V(r)=O(r^{-\kappa})$ as $r\to\infty$, for some $\kappa>2$, and study the relation between the large-time behavior of hot spots of the solutions and the behavior of the potential at the space infinity. In particular, we prove that the hot spots tend to the space infinity as $t\to\infty$ and how their rates depend on whether $V(|\cdot|)\in L^1({\bf R}^N)$ or not.

Citation

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K. Ishige. Y. Kabeya. "Hot spots for the heat equation with a rapidly decaying negative potential." Adv. Differential Equations 14 (7/8) 643 - 662, July/August 2009.

Information

Published: July/August 2009
First available in Project Euclid: 18 December 2012

zbMATH: 1182.35135
MathSciNet: MR2527688

Subjects:
Primary: 35K05, 35K15

Rights: Copyright © 2009 Khayyam Publishing, Inc.

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Vol.14 • No. 7/8 • July/August 2009
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