Differential and Integral Equations
- Differential Integral Equations
- Volume 16, Number 3 (2003), 303-326.
Exact controllability of the Boussinesq equation on a bounded domain
The purpose of this article is to study the exact boundary controllability of the classical Boussinesq equation. The control is applied to the first spatial derivative and then, to the second spatial derivative, both at the right endpoint. The exact controllability of the linearized problem is essentially proved by using the Hilbert Uniqueness Method. From this result, we deduce the exact boundary controllability for the nonlinear Boussinesq equations. The main improvements compared to existing results in the literature are the absence of restrictions on controllability time, the use of more regular spaces and the extension of the exact boundary controllability to the nonlinear Boussinesq equation.
Differential Integral Equations, Volume 16, Number 3 (2003), 303-326.
First available in Project Euclid: 21 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 93B05: Controllability
Secondary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10] 76D55: Flow control and optimization [See also 49Q10, 93C20, 93C95] 93C20: Systems governed by partial differential equations
Crépeau, Emmanuelle. Exact controllability of the Boussinesq equation on a bounded domain. Differential Integral Equations 16 (2003), no. 3, 303--326. https://projecteuclid.org/euclid.die/1356060673