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

Daniele Andreucci; Kazuhiro Ishige

doi:10.1007/s10231-011-0226-x

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

Daniele Andreucci, Kazuhiro Ishige

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	329-348
Number of pages	20
Journal	Annali di Matematica Pura ed Applicata
Volume	192
Issue number	3
DOIs	https://doi.org/10.1007/s10231-011-0226-x
Publication status	Published - 2013 Jun

Keywords

Concavity of solutions of parabolic equations
Heat equation with potential
Hot spots
Local quasi-concavity for large times

ASJC Scopus subject areas

Applied Mathematics

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10.1007/s10231-011-0226-x

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abstract = "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.",

keywords = "Concavity of solutions of parabolic equations, Heat equation with potential, Hot spots, Local quasi-concavity for large times",

author = "Daniele Andreucci and Kazuhiro Ishige",

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AU - Andreucci, Daniele

AU - Ishige, Kazuhiro

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N2 - 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.

AB - 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.

KW - Concavity of solutions of parabolic equations

KW - Heat equation with potential

KW - Hot spots

KW - Local quasi-concavity for large times

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JF - Annali di Matematica Pura ed Applicata

IS - 3

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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