# American Institute of Mathematical Sciences

August  2018, 38(8): 4041-4069. doi: 10.3934/dcds.2018176

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

 Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan

* Corresponding author: Kazuhiro Ishige

Received  November 2017 Revised  March 2018 Published  May 2018

Fund Project: The first author is partially supported by the Grant-in-Aid for Scientific Research (A)(No. 15H02058) from Japan Society for the Promotion of Science

Let $L: = -Δ+V$ be a nonnegative Schrödinger operator on $L^2({\bf R}^N)$, where $N≥ 2$ 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 $e^{-tL}\varphi$, where $\varphi∈ L^2({\bf R}^N, e^{|x|^2/4}\, dx)$.

Citation: Kazuhiro Ishige, Asato Mukai. Large time behavior of solutions of the heat equation with inverse square potential. Discrete & Continuous Dynamical Systems - A, 2018, 38 (8) : 4041-4069. doi: 10.3934/dcds.2018176
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