Differential and Integral Equations

Exact controllability of the Boussinesq equation on a bounded domain

Emmanuelle Crépeau

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Abstract

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.

Article information

Source
Differential Integral Equations, Volume 16, Number 3 (2003), 303-326.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060673

Mathematical Reviews number (MathSciNet)
MR1947955

Zentralblatt MATH identifier
1161.93302

Subjects
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

Citation

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


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