Potential well and exact boundary controllability for radial semilinear wave equations on Schwarzschild spacetime

Ning-An Lai; Jinglei Zhao

doi:10.3934/cpaa.2014.13.1317

Article Contents

2014, Volume 13, Issue 3: 1317-1325. Doi: 10.3934/cpaa.2014.13.1317

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Potential well and exact boundary controllability for radial semilinear wave equations on Schwarzschild spacetime

Ning-An Lai^1, and
Jinglei Zhao^2,

1.
Sciences College, Lishui University, Zhejiang 323000
2.
College of Education, Lishui University, Zhejinag 323000

Received: July 31, 2013

Revised: September 30, 2013

Published: April 2015

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Abstract

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.

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Mathematics Subject Classification: 35L05, 35L71, 93B05, 93C20.

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