Hot spots of solutions to the heat equation with inverse square potential

被引：4

作者：

Ishige, Kazuhiro ^{[1
]}

Kabeya, Yoshitsugu ^{[2
]}

Mukai, Asato ^{[1
]}

机构：

[1] Univ Tokyo, Grad Sch Math Sci, Tokyo, Japan

[2] Osaka Prefecture Univ, Dept Math Sci, Sakai, Osaka, Japan

来源：

APPLICABLE ANALYSIS | 2019年 / 98卷 / 10期

基金：

日本学术振兴会;

关键词：

Hot spots; heat equation; inverse square potential; LARGE TIME BEHAVIOR; KERNEL; CRITICALITY; MOVEMENT; INEQUALITY; OPERATOR; BOUNDS; DOMAIN; NORMS;

D O I：

10.1080/00036811.2018.1466284

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the large time behavior of the hot spots of the solution to the Cauchy problem where and decays quadratically as . In this paper, based on the arguments in [K. Ishige and A. Mukai, to appear in Discrete Contin. Dyn. Syst.], we classify the large time behavior of the hot spots of u and reveal the relationship between the behavior of the hot spots and the harmonic functions for .

引用

页码：1843 / 1861

页数：19

共 50 条

[31] GROUND STATE SOLUTIONS FOR HAMILTONIAN ELLIPTIC SYSTEM WITH INVERSE WITH INVERSE SQUARE POTENTIAL
Zhang, Jian
Zhang, Wen
Tang, Xianhua
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2017, 37 (08) : 4565 - 4583
[32] Observability estimate for the parabolic equations with inverse square potential
Zheng, Guojie
Ma, Baolin
AIMS MATHEMATICS, 2021, 6 (12): : 13525 - 13532
[33] Weighted Hardy's inequality and the Kolmogorov equation perturbed by an inverse-square potential
Goldstein, G. R.
Goldstein, J. A.
Rhandi, A.
APPLICABLE ANALYSIS, 2012, 91 (11) : 2057 - 2071
[34] Schauder estimates of the uniformly elliptic equation with a inverse-square potential
Li, Zijin
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 464 (02) : 1352 - 1365
[35] Coupling constant dependence for the Schrodinger equation with an inverse-square potential
Smirnov, A. G.
ADVANCES IN OPERATOR THEORY, 2021, 6 (02)
[36] Eigenfunction expansions for the Schrödinger equation with an inverse-square potential
A. G. Smirnov
Theoretical and Mathematical Physics, 2016, 187 : 762 - 781
[37] DYNAMICS OF THRESHOLD SOLUTIONS FOR ENERGY CRITICAL NLS WITH INVERSE SQUARE POTENTIAL
Yang, Kai
Zeng, Chongchun
Zhang, Xiaoyi
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2022, 54 (01) : 173 - 219
[38] Dynamics of threshold solutions for energy critical NLW with inverse square potential
Yang, Kai
Zhang, Xiaoyi
MATHEMATISCHE ZEITSCHRIFT, 2022, 302 (01) : 353 - 389
[39] Dynamics of threshold solutions for energy critical NLW with inverse square potential
Kai Yang
Xiaoyi Zhang
Mathematische Zeitschrift, 2022, 302 : 353 - 389
[40] Blow-up of positive solutions for the semilinear heat equation with a potential
Zhang, Kaiqiang
APPLICABLE ANALYSIS, 2024, 103 (05) : 954 - 969

← 1 2 3 4 5 →