Remark on the Cauchy problem for the evolution p-Laplacian equation

被引：0

作者：

Wang, Liangwei ^{[1
]}

Yin, Jngxue ^{[2
]}

Cao, Jinde ^{[3
,4
]}

机构：

[1] Chongqing Three Gorges Univ, Sch Math & Stat, 666 Tian Xing Rd, Chongqing 404100, Peoples R China

[2] South China Normal Univ, Sch Math Sci, 55 West Zhong Shan Rd, Guangzhou 510631, Guangdong, Peoples R China

[3] Southeast Univ, Sch Math, 2 Southeast Univ Rd, Nanjing 210996, Jiangsu, Peoples R China

[4] Southeast Univ, Res Ctr Complex Syst & Network Sci, 2 Southeast Univ Rd, Nanjing 210996, Jiangsu, Peoples R China

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2017年

基金：

中国国家自然科学基金;

关键词：

chaos; evolution p-Laplacian equation; Cauchy problem; propagation estimate; decay estimate; PERTURBED NLS SYSTEMS; HOMOCLINIC ORBITS; NAVIER-STOKES; CHAOS; COMPLEXITY; BEHAVIOR;

D O I：

10.1186/s13660-017-1449-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove that the semigroup S(t) generated by the Cauchy problem of the evolution p-Laplacian equation partial derivative u/partial derivative t - div(|del u|(p-2)del u) = 0 (p > 2) is continuous form a weighted L-infinity space to the continuous space C-0(R-N). Then we use this property to reveal the fact that the evolution p-Laplacian equation generates a chaotic dynamical system on some compact subsets of C-0(R-N). For this purpose, we need to establish the propagation estimates and the space-time decay estimates for the solutions first.

引用

页数：16

共 31 条

[1] ON DEVANEY DEFINITION OF CHAOS [J].