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

Kazuhiro Ishige, Yoshitsugu Kabeya, Asato Mukai

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We investigate the large time behavior of the hot spots of the solution to the Cauchy problem (Formula presented.) where (Formula presented.) and V = V(r) decays quadratically as r → ∞. In this paper, based on the arguments in [K. Ishige and A. Mukai, to appear in Discrete Contin. Dyn. Syst.], 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 - ∆ + V.

Original languageEnglish
Pages (from-to)1843-1861
Number of pages19
JournalApplicable Analysis
Volume98
Issue number10
DOIs
Publication statusPublished - 2019 Jul 27

Keywords

  • 35K05
  • 35K15
  • Hot spots
  • heat equation
  • inverse square potential

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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