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arXiv · 1802.00175

Hot spots of solutions to the heat equation with inverse square potential

Kazuhiro Ishige·Yoshitsugu Kabeya·Asato Mukai
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Abstract

We investigate the large time behavior of the hot spots of the solution to the Cauchy problem for the heat equation with a potential $\partial_t u-\Delta u+V(|x|)u=0$, where $V=V(r)$ decays quadratically as $r\to\infty$. In this paper, based on the arguments in [K. Ishige and A. Mukai, preprint (arXiv:1709.00809)], we classify the large time behavior of the hot spots of $u$ and reveal the relationship between the behavior of the hot spots and the harmonic functions for $-\Delta+V$.

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Kazuhiro Ishige, Yoshitsugu Kabeya, Asato Mukai. 2018-02-01. Hot spots of solutions to the heat equation with inverse square potential. https://arxiv.org/abs/1802.00175

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