arXiv subjects

Asato Mukai

Publications and source records attributed to Asato Mukai.

2 recordsLinked to original sources

arXiv2018

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

We investigate the large time behavior of the hot spots of the solution to the Cauchy problem for the heat equation with a potential $\partial_t u-Δu+V(|x|)u=0$, 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 $-Δ+V$.

math.AP↗

arXiv2017

Large time behavior of solutions of the heat equation with inverse square potential

Let $L:=-Δ+V$ be a nonnegative Schrödinger operator on $L^2({\bf R}^N)$, where $N\ge 2$ and $V$ is a radially symmetric inverse square potential. In this paper we assume either $L$ is subcritical or null-critical and we establish a method for obtaining the precise description of the large time behavior of $e^{-tL}φ$, where $φ\in L^2({\bf R}^N,e^{|x|^2/4}\,dx)$.

math.AP↗