Blow-up of Solutions of Nonlinear Heat Equation with Hypoelliptic Operators on Graded Lie Groups

被引：3

作者：

Bekbolat, Bayan ^{[1
,2
,3
]}

Kassymov, Aidyn ^{[1
,2
,3
]}

Tokmagambetov, Niyaz ^{[1
,2
,3
]}

机构：

[1] Inst Math & Math Modeling, Alma Ata, Kazakhstan

[2] Al Farabi Kazakh Natl Univ, 71 Al Farabi Ave, Alma Ata, Kazakhstan

[3] Univ Ghent, Dept Math Anal Log & Discrete Math, Ghent, Belgium

来源：

COMPLEX ANALYSIS AND OPERATOR THEORY | 2019年 / 13卷 / 07期

关键词：

Rockland operator; Hypoelliptic operator; Nonlinear heat equation; A graded Lie group; Blow-up; Fujita exponent; EVOLUTION-EQUATIONS; ROCKLAND OPERATORS; NONEXISTENCE;

D O I：

10.1007/s11785-019-00940-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we show blow-up of solutions of the nonlinear heat equation with the Rockland operators on the graded Lie groups. In addition, we give the necessary conditions for the existence of local or global solutions of the nonlinear heat equation with hypoelliptic operators on Heisenberg groups.

引用

页码：3347 / 3357

页数：11

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[2]

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[3]

Fischer V., 2014, ARXIV14116950

[4]

Fischer V, 2016, QUANTIZATION NILPOTE