an:01422889
Zbl 0951.35108
Lee, Hyung-Chun; Shin, Byeong Chun
Piecewise optimal distributed controls for 2D Boussinesq equations
EN
Math. Methods Appl. Sci. 23, No. 3, 227-254 (2000).
0170-4214 1099-1476
2000
j
35Q30 35B37 35B40 49M25
velocity and temperature tracking problem for viscous incompressible thermally convected flows; Boussinesq equations; piecewise optimal control problem; semidiscrete approximation
The authors consider the velocity and temperature tracking problem for viscous incompressible thermally convected flows in two dimensions (which is similar to the velocity tracking problem for viscous incompressible flows). This problem is formulated as a piecewise (in time) distributed optimal control problem for the Boussinesq equations. The semidiscrete (in time) approximation of the piecewise optimal control problem is also studied. The main theorem asserts that the \(L^2\) and \(H^1\) norms of the difference between the controlled state and the desired state both decay to zero exponentially in time. A similar result is obtained for the semidiscrete approximation of the piecewise optimal control problem.
C.Popa (Iaşi)