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

  • * Corresponding author: Kazuhiro Ishige

    * Corresponding author: Kazuhiro Ishige 

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

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  • 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 $\varphi∈ L^2({\bf R}^N, e^{|x|^2/4}\, dx)$.

    Mathematics Subject Classification: Primary: 35K15, 35B40; Secondary: 35K67.


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