Large time behavior of solutions of the heat equation with inverse square potential

Kazuhiro Ishige; Asato Mukai

doi:10.3934/dcds.2018176

Large time behavior of solutions of the heat equation with inverse square potential

Kazuhiro Ishige, Asato Mukai

SCI - Mathematics

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

2 Citations (Scopus)

Abstract

Abstract. Let L := −∆ + V be a nonnegative Schrödinger operator on L²(R^N), where N ≥ 2 and V is a radially symmetric inverse square potential. In this paper we assume either L is subcritical or null-critical and we establish a method for obtaining the precise description of the large time behavior of e^−tLϕ, where ϕ ∈ L²(R^N, e^|x^|^2/4 dx).

Original language	English
Pages (from-to)	4041-4069
Number of pages	29
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	38
Issue number	8
DOIs	https://doi.org/10.3934/dcds.2018176
Publication status	Published - 2018 Aug

Keywords

Inverse square potential
Large time behavior
Schrödinger operator

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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@article{6545b62dc39b47069b7a0d90fbc4e953,

title = "Large time behavior of solutions of the heat equation with inverse square potential",

abstract = "Abstract. Let L := −∆ + V be a nonnegative Schr{\"o}dinger operator on L2(RN), where N ≥ 2 and V is a radially symmetric inverse square potential. In this paper we assume either L is subcritical or null-critical and we establish a method for obtaining the precise description of the large time behavior of e−tLϕ, where ϕ ∈ L2(RN, e|x|2/4 dx).",

keywords = "Inverse square potential, Large time behavior, Schr{\"o}dinger operator",

author = "Kazuhiro Ishige and Asato Mukai",

note = "Funding Information: 2010 Mathematics Subject Classification. Primary: 35K15, 35B40; Secondary: 35K67. Key words and phrases. Schr{\"o}dinger operator, inverse square potential, large time behavior. The first author is partially supported by the Grant-in-Aid for Scientific Research (A)(No. 15H02058) from Japan Society for the Promotion of Science. ∗ Corresponding author: Kazuhiro Ishige. Funding Information: The first author is partially supported by the Grant-in-Aid for Scientific Research (A)(No. 15H02058) from Japan Society for the Promotion of Science. The first author would like to thank Professor Yehuda Pinchover for his valuable comments. Publisher Copyright: {\textcopyright} 2018 American Institute of Mathematical Sciences. All Rights Reserved. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.",

year = "2018",

month = aug,

doi = "10.3934/dcds.2018176",

language = "English",

volume = "38",

pages = "4041--4069",

journal = "Discrete and Continuous Dynamical Systems",

issn = "1078-0947",

publisher = "Southwest Missouri State University",

number = "8",

}

TY - JOUR

T1 - Large time behavior of solutions of the heat equation with inverse square potential

AU - Ishige, Kazuhiro

AU - Mukai, Asato

N1 - Funding Information: 2010 Mathematics Subject Classification. Primary: 35K15, 35B40; Secondary: 35K67. Key words and phrases. Schrödinger operator, inverse square potential, large time behavior. The first author is partially supported by the Grant-in-Aid for Scientific Research (A)(No. 15H02058) from Japan Society for the Promotion of Science. ∗ Corresponding author: Kazuhiro Ishige. Funding Information: The first author is partially supported by the Grant-in-Aid for Scientific Research (A)(No. 15H02058) from Japan Society for the Promotion of Science. The first author would like to thank Professor Yehuda Pinchover for his valuable comments. Publisher Copyright: © 2018 American Institute of Mathematical Sciences. All Rights Reserved. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2018/8

Y1 - 2018/8

N2 - Abstract. Let L := −∆ + V be a nonnegative Schrödinger operator on L2(RN), where N ≥ 2 and V is a radially symmetric inverse square potential. In this paper we assume either L is subcritical or null-critical and we establish a method for obtaining the precise description of the large time behavior of e−tLϕ, where ϕ ∈ L2(RN, e|x|2/4 dx).

AB - Abstract. Let L := −∆ + V be a nonnegative Schrödinger operator on L2(RN), where N ≥ 2 and V is a radially symmetric inverse square potential. In this paper we assume either L is subcritical or null-critical and we establish a method for obtaining the precise description of the large time behavior of e−tLϕ, where ϕ ∈ L2(RN, e|x|2/4 dx).

KW - Inverse square potential

KW - Large time behavior

KW - Schrödinger operator

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U2 - 10.3934/dcds.2018176

DO - 10.3934/dcds.2018176

M3 - Article

AN - SCOPUS:85048038551

VL - 38

SP - 4041

EP - 4069

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

SN - 1078-0947

IS - 8

ER -

Large time behavior of solutions of the heat equation with inverse square potential

Abstract

Keywords

ASJC Scopus subject areas

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