| Title:
|
Exact controllability of the wave equation with mixed boundary condition and time-dependent coefficients (English) |
| Author:
|
Cavalcanti, M. M. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
35 |
| Issue:
|
1 |
| Year:
|
1999 |
| Pages:
|
29-57 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
wave equation |
| Keyword:
|
boundary value problem |
| Keyword:
|
exact controllability |
| Keyword:
|
Dirichlet-Neumann condition |
| MSC:
|
35B35 |
| MSC:
|
35B40 |
| MSC:
|
35L05 |
| MSC:
|
35L99 |
| MSC:
|
93B05 |
| MSC:
|
93C20 |
| idZBL:
|
Zbl 1046.35013 |
| idMR:
|
MR1684521 |
| . |
| Date available:
|
2008-06-06T22:22:34Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107683 |
| . |
| Reference:
|
[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 |
| Reference:
|
[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. Zbl 0786.93009, MR 1178650 |
| Reference:
|
[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. Zbl 0843.35009, MR 1176016 |
| Reference:
|
[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 |
| Reference:
|
[5] Fuentes Apolaya R.: Exact Controllability for temporally wave equation.Portugaliae Math., (1994), 475-488. MR 1313160 |
| Reference:
|
[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 |
| Reference:
|
[7] Komornik V.: Contrôlabilité exacte en un temps minimal.C.R.A.S. Paris, 304 (1987), 223-235. Zbl 0611.49027, MR 0883479 |
| Reference:
|
[8] Komornik V.: Exact Controllability in short time for wave equation.Ann. Inst. Henri Poincaré, 6 (1989), 153-164. MR 0991876 |
| Reference:
|
[9] Lagnese J.: Control of wave processes with distributed controls supported on a subregion.Siam J. Control and Optmin. 21 (1983), 68-85. Zbl 0512.93014, MR 0688440 |
| Reference:
|
[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 |
| Reference:
|
[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. Zbl 0375.93029, MR 0477480 |
| Reference:
|
[12] Lagnese J., Lions J. L.: Modelling, Analysis and Exact Controllability of Thin Plates.RMA Collection, N.6, Masson, Paris, (1988). MR 0953313 |
| Reference:
|
[13] Lasiecka I., Triggiani R.: Exact Controllability for the wave equation with Neumann boundary Control.Appl. Math. Optim. 19 (1989), 243-290. MR 0974187 |
| Reference:
|
[14] Lions J. L.: Controlabilité Exacte, Perturbations et Stabilization de Systèmes Distribués.Tome 1, Masson, Paris, (1988). MR 0953547 |
| . |
