Local quasi-concavity of the solutions of the heat equation with a nonnegative potential

Daniele Andreucci, Kazuhiro Ishige

研究成果: Article査読

2 被引用数 (Scopus)

抄録

In this paper we consider the Cauchy problem for the heat equation with a nonnegative potential decaying quadratically at the space infinity and investigate local concavity properties of the solution. In particular, we give a sufficient condition for the solution to be quasi-concave in a ball for any sufficiently large t, and discuss the optimality of the sufficient condition, identifying a threshold for the occurrence of local quasi-concavity.

本文言語English
ページ(範囲)329-348
ページ数20
ジャーナルAnnali di Matematica Pura ed Applicata
192
3
DOI
出版ステータスPublished - 2013 6

ASJC Scopus subject areas

  • 応用数学

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