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 -