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

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  • We consider the Cauchy problem of the two dimensional heat equation with a radially symmetric, negative potential $-V$ which behaves like $V(r)=O(r^{-\kappa})$ as $r\to\infty$, for some $\kappa > 2$. We study the rate and the direction for hot spots to tend to the spatial infinity. Furthermore we give a sufficient condition for hot spots to consist of only one point for any sufficiently large $t>0$.
    Mathematics Subject Classification: Primary: 35B05, 35B40, 35K05; Secondary: 53C35.

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