L p norms of nonnegative Schrödinger heat semigroup and the large time behavior of hot spots

Kazuhiro Ishige, Yoshitsugu Kabeya

研究成果: Article査読

15 被引用数 (Scopus)

抄録

This paper is concerned with the Cauchy problem for the heat equation with a potential(P){∂tu=δu-V(|x|)uin R N×(0,∞),u(x,0)=φ(x)in R N, where ∂ t=∂/∂t, N≥3, φ∈L 2(R N), and V=V(|x|) is a smooth, nonpositive, and radially symmetric function having quadratic decay at the space infinity. In this paper we assume that the Schrödinger operator H=-δ+V is nonnegative on L 2(R N), and give the exact power decay rates of L q norm (q≥2) of the solution e -tHφ of (P) as t→∞. Furthermore we study the large time behavior of the solution of (P) and its hot spots.

本文言語English
ページ(範囲)2695-2733
ページ数39
ジャーナルJournal of Functional Analysis
262
6
DOI
出版ステータスPublished - 2012 3 15

ASJC Scopus subject areas

  • 分析

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