Advances in Differential Equations
- Adv. Differential Equations
- Volume 16, Number 11/12 (2011), 1021-1047.
Potential well and exact boundary controllability for semilinear wave equations
In this paper, we consider the exact boundary controllability for cubic focusing semilinear wave equations in $1\le n\le 3$ space dimensions. 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, in one space dimension, the control time can be that of the linear wave equation.
Adv. Differential Equations Volume 16, Number 11/12 (2011), 1021-1047.
First available in Project Euclid: 17 December 2012
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35L05: Wave equation
Zhou, Yi; Lai, Ning-An. Potential well and exact boundary controllability for semilinear wave equations. Adv. Differential Equations 16 (2011), no. 11/12, 1021--1047. https://projecteuclid.org/euclid.ade/1355703111