Large time behaviors of hot spots for the heat equation with a potential

Kazuhiro Ishige; Yoshitsugu Kabeya

doi:10.1016/j.jde.2008.02.027

Large time behaviors of hot spots for the heat equation with a potential

Kazuhiro Ishige, Yoshitsugu Kabeya

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

17 Citations (Scopus)

Abstract

We consider the Cauchy problem of the heat equation with a potential which behaves like the inverse square at infinity. In this paper we study the large time behavior of hot spots of the solutions for the Cauchy problem, by using the asymptotic behavior of the potential at the space infinity.

Original language	English
Pages (from-to)	2934-2962
Number of pages	29
Journal	Journal of Differential Equations
Volume	244
Issue number	11
DOIs	https://doi.org/10.1016/j.jde.2008.02.027
Publication status	Published - 2008 Jun 1
Externally published	Yes

Keywords

Asymptotic behavior
Harmonic functions
Heat equations
Hot spots
Potential

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2008.02.027

Cite this

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title = "Large time behaviors of hot spots for the heat equation with a potential",

abstract = "We consider the Cauchy problem of the heat equation with a potential which behaves like the inverse square at infinity. In this paper we study the large time behavior of hot spots of the solutions for the Cauchy problem, by using the asymptotic behavior of the potential at the space infinity.",

keywords = "Asymptotic behavior, Harmonic functions, Heat equations, Hot spots, Potential",

author = "Kazuhiro Ishige and Yoshitsugu Kabeya",

note = "Funding Information: * Corresponding author. E-mail addresses: ishige@math.tohoku.ac.jp (K. Ishige), kabeya@ms.osakafu-u.ac.jp (Y. Kabeya). 1 Supported in part by the Grant-in-Aid for Scientific Research (B) (No. 19340036), Japan Society for the Promotion of Science. 2 Supported in part by the Grant-in-Aid for Scientific Research (C) (No. 19540224), Japan Society for the Promotion of Science.",

year = "2008",

month = jun,

day = "1",

doi = "10.1016/j.jde.2008.02.027",

language = "English",

volume = "244",

pages = "2934--2962",

journal = "Journal of Differential Equations",

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T1 - Large time behaviors of hot spots for the heat equation with a potential

AU - Ishige, Kazuhiro

AU - Kabeya, Yoshitsugu

N1 - Funding Information: * Corresponding author. E-mail addresses: ishige@math.tohoku.ac.jp (K. Ishige), kabeya@ms.osakafu-u.ac.jp (Y. Kabeya). 1 Supported in part by the Grant-in-Aid for Scientific Research (B) (No. 19340036), Japan Society for the Promotion of Science. 2 Supported in part by the Grant-in-Aid for Scientific Research (C) (No. 19540224), Japan Society for the Promotion of Science.

PY - 2008/6/1

Y1 - 2008/6/1

N2 - We consider the Cauchy problem of the heat equation with a potential which behaves like the inverse square at infinity. In this paper we study the large time behavior of hot spots of the solutions for the Cauchy problem, by using the asymptotic behavior of the potential at the space infinity.

AB - We consider the Cauchy problem of the heat equation with a potential which behaves like the inverse square at infinity. In this paper we study the large time behavior of hot spots of the solutions for the Cauchy problem, by using the asymptotic behavior of the potential at the space infinity.

KW - Asymptotic behavior

KW - Harmonic functions

KW - Heat equations

KW - Hot spots

KW - Potential

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EP - 2962

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 11

ER -

Large time behaviors of hot spots for the heat equation with a potential

Abstract

Keywords

ASJC Scopus subject areas

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