标题： 热方程带有倒数平方势的解的热点 显示英文标题

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

摘要： 我们研究热方程带势函数 $\partial_t u-\Delta u+V(|x|)u=0$的柯西问题解的热点在长时间行为，其中 $V=V(r)$随着 $r\to\infty$的二次方衰减。 在本文中，基于 [K. Ishige 和 A. Mukai, 预印本 (arXiv:1709.00809)] 中的论证，我们对 $u$的热点长时间行为进行分类，并揭示热点行为与 $-\Delta+V$的调和函数之间的关系。 显示英文摘要

摘要： 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 $-\Delta+V$.