Hot spots for the two dimensional heat equation with a rapidly decaying negative potential

Kazuhiro Ishige; Yoshitsugu Kabeya

doi:10.3934/dcdss.2011.4.833

Hot spots for the two dimensional heat equation with a rapidly decaying negative potential

Kazuhiro Ishige, Yoshitsugu Kabeya

SCI - Mathematics

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

5 Citations (Scopus)

Abstract

We consider the Cauchy problem of the two dimensional heat equation with a radially symmetric, negative potential -V which behaves like V (r) = O(r ^-κ) as r → ∞, for some κ > 2. We study the rate and the direction for hot spots to tend to the spatial infinity. Furthermore we give a sufficient condition for hot spots to consist of only one point for any sufficiently large t > 0.

Original language	English
Pages (from-to)	833-849
Number of pages	17
Journal	Discrete and Continuous Dynamical Systems - Series S
Volume	4
Issue number	4
DOIs	https://doi.org/10.3934/dcdss.2011.4.833
Publication status	Published - 2011 Aug

Keywords

Heat equation
Hot spots
Large time behavior

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.3934/dcdss.2011.4.833

Cite this

@article{7ecad493cd464152a23a5900808fe880,

title = "Hot spots for the two dimensional heat equation with a rapidly decaying negative potential",

abstract = "We consider the Cauchy problem of the two dimensional heat equation with a radially symmetric, negative potential -V which behaves like V (r) = O(r -κ) as r → ∞, for some κ > 2. We study the rate and the direction for hot spots to tend to the spatial infinity. Furthermore we give a sufficient condition for hot spots to consist of only one point for any sufficiently large t > 0.",

keywords = "Heat equation, Hot spots, Large time behavior",

author = "Kazuhiro Ishige and Yoshitsugu Kabeya",

year = "2011",

month = aug,

doi = "10.3934/dcdss.2011.4.833",

language = "English",

volume = "4",

pages = "833--849",

journal = "Discrete and Continuous Dynamical Systems - Series S",

issn = "1937-1632",

publisher = "American Institute of Mathematical Sciences",

number = "4",

}

TY - JOUR

T1 - Hot spots for the two dimensional heat equation with a rapidly decaying negative potential

AU - Ishige, Kazuhiro

AU - Kabeya, Yoshitsugu

PY - 2011/8

Y1 - 2011/8

N2 - We consider the Cauchy problem of the two dimensional heat equation with a radially symmetric, negative potential -V which behaves like V (r) = O(r -κ) as r → ∞, for some κ > 2. We study the rate and the direction for hot spots to tend to the spatial infinity. Furthermore we give a sufficient condition for hot spots to consist of only one point for any sufficiently large t > 0.

AB - We consider the Cauchy problem of the two dimensional heat equation with a radially symmetric, negative potential -V which behaves like V (r) = O(r -κ) as r → ∞, for some κ > 2. We study the rate and the direction for hot spots to tend to the spatial infinity. Furthermore we give a sufficient condition for hot spots to consist of only one point for any sufficiently large t > 0.

KW - Heat equation

KW - Hot spots

KW - Large time behavior

UR - http://www.scopus.com/inward/record.url?scp=84856286523&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84856286523&partnerID=8YFLogxK

U2 - 10.3934/dcdss.2011.4.833

DO - 10.3934/dcdss.2011.4.833

M3 - Article

AN - SCOPUS:84856286523

SN - 1937-1632

VL - 4

SP - 833

EP - 849

JO - Discrete and Continuous Dynamical Systems - Series S

JF - Discrete and Continuous Dynamical Systems - Series S

IS - 4

ER -

Hot spots for the two dimensional heat equation with a rapidly decaying negative potential

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this