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

2017/09/04 by Kazuhiro Ishige, Ishige, Kazuhiro, Asato Mukai +1 · 1 citation
Mathematics · #35B40 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Primary 35K15 #Secondary 35K67 #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1709.00809

openalex publication_date 2017/09/04 · openalex created_date 2017/09/15 · openalex updated_date 2026/07/28

Abstract

Let L:=-Δ+V be a nonnegative Schrödinger operator on L²(\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^-tLφ, where φ∈ L²(\bf R^N,e^|x|2/4 dx).

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

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