Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
wave equation; boundary value problem; exact controllability; Dirichlet-Neumann condition
wave equation; boundary value problem; exact controllability; Dirichlet-Neumann condition
Summary:
In this paper we study the boundary exact controllability for the equation \[ \frac{\partial }{\partial t}\left(\alpha (t){{\partial y}\over { \partial t}}\right)-\sum _{j=1}^n{{\partial }\over {\partial x_j}}\left(\beta (t)a(x){{\partial y}\over {\partial x_j}}\right)=0\;\;\;\hbox{in}\;\; \Omega \times (0,T)\,, \] when the control action is of Dirichlet-Neumann form and $\Omega $ is a bounded domain in ${R}^n$. The result is obtained by applying the HUM (Hilbert Uniqueness Method) due to J. L. Lions.
References:
[1] Bardos C., Cheng C.: Control and stabilization for the wave equation, part III : domain with moving boundary. Siam J. Control and Optim., 19 (1981), 123-138. MR 0603085
[2] Bardos C., Lebeau G., Rauch J.: Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary. Siam J. Control and Optim., 30, N.5 (1992), 1024-1065. MR 1178650 | Zbl 0786.93009
[3] Cioranescu D., Donato P., Zuazua E.: Exact Boundary Controllability for the wave equation in domains with small holes. J. Math. Pures Appl. 71 (1992), 343-357. MR 1176016 | Zbl 0843.35009
[4] Coron J. M.: Contrôlabilité exacte frontière de l’ équacion d’ Euler des fluides parfais incompressibles bidimensionnels. C.R.A.S. Paris, 317 (1993) S.I, 271-276. MR 1233425
[5] Fuentes Apolaya R.: Exact Controllability for temporally wave equation. Portugaliae Math., (1994), 475-488. MR 1313160
[6] Grisvard P.: Contrôlabilité exacte des solutions de l’équacion des ondes en présence de singularités. J. Math. pure et appl., 68 (1989), 215-259. MR 1010769
[7] Komornik V.: Contrôlabilité exacte en un temps minimal. C.R.A.S. Paris, 304 (1987), 223-235. MR 0883479 | Zbl 0611.49027
[8] Komornik V.: Exact Controllability in short time for wave equation. Ann. Inst. Henri Poincaré, 6 (1989), 153-164. MR 0991876
[9] Lagnese J.: Control of wave processes with distributed controls supported on a subregion. Siam J. Control and Optmin. 21 (1983), 68-85. MR 0688440 | Zbl 0512.93014
[10] Lagnese J.: Boundary Patch control of the wave equation in some non-star complemeted regions. J. Math. Anal. 77 (1980) 364-380. MR 0593220
[11] Lagnese J.: Boundary Value Control of a Class of Hyperbolic Equations in a General Region. Siam J. Control and Optim., 15, N.6 (1977), 973-983. MR 0477480 | Zbl 0375.93029
[12] Lagnese J., Lions J. L.: Modelling, Analysis and Exact Controllability of Thin Plates. RMA Collection, N.6, Masson, Paris, (1988). MR 0953313
[13] Lasiecka I., Triggiani R.: Exact Controllability for the wave equation with Neumann boundary Control. Appl. Math. Optim. 19 (1989), 243-290. MR 0974187
[14] Lions J. L.: Controlabilité Exacte, Perturbations et Stabilization de Systèmes Distribués. Tome 1, Masson, Paris, (1988). MR 0953547
Search
Partner of
