### Potential well and exact boundary controllability for semilinear wave equations

#### Abstract

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.

#### Article information

Source
Adv. Differential Equations Volume 16, Number 11/12 (2011), 1021-1047.

Dates
First available in Project Euclid: 17 December 2012