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

2018/02/01 by Kazuhiro Ishige, Ishige, Kazuhiro, Yoshitsugu Kabeya +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1802.00175

openalex publication_date 2018/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the large time behavior of the hot spots of the solution to the Cauchy problem for the heat equation with a potential ∂_t u-Δu+V(|x|)u=0, where V=V(r) decays quadratically as r→∞. 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.

Citations

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

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