IJPAM: Volume 35, No. 2 (2007)

CONTROLLABILITY WITH TARGET STATE
ON THE BOUNDARY

A. Boutoulout$^1$, L. Badraoui$^2$, H. Bourray$^3$
$^1$Department of Mathematics and Computer Science
Faculty of Sciences
Moulay Ismail University
P.O. Box 11201, Meknes, MOROCCO
e-mail: aliboutoulout@yahoo.fr
$^2$Royal Naval School
MOROCCO
e-mail: badraoui@emi.ac.ma
$^3$Faculty of Poly Disciplinary
Moulay Ismail University
Errachidia, MOROCCO
e-mail: hbourrayh@yahoo.fr


Abstract.Various aspects of the boundary regional controllability (when the target state to be reached is given in a subregion of the boundary) introduced in [#!8!#] have been discussed in [#!1!#] for the heat equation, in [#!3!#] for parabolic systems and in [#!18!#] for hyperbolic systems. In this paper we consider the system:

\begin{displaymath}\left\{
\begin{array}{ll}
\displaystyle\frac{\partial y}{\par...
... [0,T]\,,\\
y(x,0) = y_0(x)\,, & \Omega\,.
\end{array}\right.
\end{displaymath}

An approach to the general problem of this kind is given and an approximation method to calculate the optimal solution is proposed. This approach uses a result relating to the null controllability from [11] and consequently according to [12] and establishes at the same time the time-invariance of reachable states set.

Received: November 17, 2006

AMS Subject Classification: 26A33

Key Words and Phrases: controllability, boundary target, control function, parabolic systems

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 35
Issue: 2