LOCAL EXACT BOUNDARY CONTROLLABILITY OF THE BOUSSINESQ EQUATION

Citation
Av. Fursikov et Oy. Imanuvilov, LOCAL EXACT BOUNDARY CONTROLLABILITY OF THE BOUSSINESQ EQUATION, SIAM journal on control and optimization, 36(2), 1998, pp. 391-421
Citations number
38
Categorie Soggetti
Mathematics,"Robotics & Automatic Control",Mathematics,"Robotics & Automatic Control
ISSN journal
03630129
Volume
36
Issue
2
Year of publication
1998
Pages
391 - 421
Database
ISI
SICI code
0363-0129(1998)36:2<391:LEBCOT>2.0.ZU;2-S
Abstract
We study the local exact boundary controllability problem for the Bous sinesq equations that describe an incompressible fluid ow coupled to t hermal dynamics. The result that we get in this paper is as follows: s uppose that (y) over cap(t, x) is a given solution of the Boussinesq e quation where t is an element of (0, T), x is an element of Omega, Ome ga is a bounded domain with C-infinity-boundary partial derivative Ome ga. Let y(0)(x) be a given initial condition and \\(y) over cap 0, .) - y(0)\\ < epsilon where epsilon = epsilon((y) over cap) is small enou gh. Then there exists boundary control u such that the solution y(t; x ) of the Boussinesq equations satisfying y\((0, T) x partial derivativ e Omega) = u, y\(t=0) = y(0) coincides with (y) over cap(t, x) at the instant T : y(T;x) = (y) over cap(T, x).