Advances in Differential Equations

Hot spots for the heat equation with a rapidly decaying negative potential

K. Ishige and Y. Kabeya

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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.

Article information

Adv. Differential Equations, Volume 14, Number 7/8 (2009), 643-662.

First available in Project Euclid: 18 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K05: Heat equation 35K15: Initial value problems for second-order parabolic equations


Ishige, K.; Kabeya, Y. Hot spots for the heat equation with a rapidly decaying negative potential. Adv. Differential Equations 14 (2009), no. 7/8, 643--662.

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