POTENTIAL WELL AND EXACT BOUNDARY CONTROLLABILITY FOR RADIAL SEMILINEAR WAVE EQUATIONS ON SCHWARZSCHILD SPACETIME

被引：0

作者：

Lai, Ning-An ^{[1
]}

Zhao, Jinglei ^{[2
]}

机构：

[1] Lishui Univ, Coll Sci, Lishui 323000, Zhejiang, Peoples R China

[2] Lishui Univ, Coll Educ, Zhejinag 323000, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2014年 / 13卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Semilinear wave equation; Schwarzschild spacetime; exact boundary controllability; potential well; SCATTERING;

D O I：

10.3934/cpaa.2014.13.1317

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the exact boundary controllability for the cubic focusing semilinear wave equation on Schwarzschild black hole background in radially symmetrical case. When the initial data and the final data are in the so called potential well, we find that the sufficient condition for the global existence is also sufficient to ensure the exact boundary controllability of the problem. Moreover, under the assumption of radial symmetry, our problem is changed to one space dimension case, and then the control time can be that of the linear wave equation.

引用

页码：1317 / 1325

页数：9