| Title:
|
Controllability of functional differential systems of Sobolev type in Banach spaces (English) |
| Author:
|
Balachandran, Krishnan |
| Author:
|
Dauer, Jerald P. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
34 |
| Issue:
|
3 |
| Year:
|
1998 |
| Pages:
|
[349]-357 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Sufficient conditions for controllability of partial functional differential systems of Sobolev type in Banach spaces are established. The results are obtained using compact semigroups and the Schauder fixed point theorem. An example is provided to illustrate the results. (English) |
| Keyword:
|
controllability |
| Keyword:
|
Banach space |
| Keyword:
|
differential system of Sobolev type |
| MSC:
|
34G20 |
| MSC:
|
93B05 |
| MSC:
|
93C25 |
| idZBL:
|
Zbl 1274.93031 |
| idMR:
|
MR1640907 |
| . |
| Date available:
|
2009-09-24T19:16:46Z |
| Last updated:
|
2015-03-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135212 |
| . |
| Reference:
|
[1] Balachandran K., Balasubramaniam P., Dauer J. P.: Controllability of nonlinear integrodifferential systems in Banach space.J. Optim. Theory Appl. 84 (1995), 83–91 Zbl 0821.93010, MR 1312963, 10.1007/BF02191736 |
| Reference:
|
[2] Balachandran K., Balasubramaniam P., Dauer J. P.: Controllability of quasilinear delay systems in Banach spaces.Optimal Control Appl. Methods 16 (1995), 283–290 MR 1349807 |
| Reference:
|
[3] Balachandran K., Balasubramaniam P., Dauer J. P.: Local null controllability of nonlinear functional differential systems in Banach spaces.J. Optim. Theory Appl. 88 (1996), 61–75 MR 1367033, 10.1007/BF02192022 |
| Reference:
|
[4] Brill H.: A semilinear Sobolev equation in Banach space.J. Differential Equations 24 (1977), 412–425 MR 0466818, 10.1016/0022-0396(77)90009-2 |
| Reference:
|
[5] Chuckwu E. N., Lenhart S. M.: Controllability questions for nonlinear systems in abstract spaces.J. Optim. Theory Appl. 68 (1991), 437–462 MR 1097312, 10.1007/BF00940064 |
| Reference:
|
[6] Curtain R. F., Prichard A. J.: Infinite Dimensional Linear Systems Theory.Springer–Verlag, New York 1978 MR 0516812 |
| Reference:
|
[7] Kartsatos A. C., Parrott M. E.: On a class of nonlinear functional pseudoparabolic problems.Funkcial. Ekvac. 25 (1982), 207–221 Zbl 0507.34064, MR 0694913 |
| Reference:
|
[8] Kwun Y. C., Park J. Y., Ryu J. W.: Approximate controllability and controllability for delay Volterra systems.Bull. Korean Math. Soc. 28 (1991), 131–145 MR 1127732 |
| Reference:
|
[9] Lagnese J.: General boundary value problems for differential equations of Sobolov type.SIAM J. Math. Anal. 3 (1972) 105–119 MR 0333422, 10.1137/0503013 |
| Reference:
|
[10] Lasiecka I., Triggiani R.: Exact controllability of semilinear abstract systems with application to waves and plates bounadry control problems.Appl. Math. Optim. 23 (1991), 109–154 MR 1086465, 10.1007/BF01442394 |
| Reference:
|
[11] Lightbourne J. H., Rankin S. M.: A partial functional differential equation of Sobolev type.J. Math. Anal. Appl. 93 (1983), 328–337 Zbl 0519.35074, MR 0700149, 10.1016/0022-247X(83)90178-6 |
| Reference:
|
[12] Nakagiri S., Yamamoto R.: Controllability and observability of linear retarded systems in Banach spaces.Internat. J. Control 49 (1989), 1489–1504 Zbl 0676.93029, MR 0998053, 10.1080/00207178908559721 |
| Reference:
|
[13] Naito K.: Approximate controllability for trajectories of semilinear control systems.J. Optim. Theory Appl. 6 (1989), 57–65 Zbl 0632.93007, MR 0981945, 10.1007/BF00938799 |
| Reference:
|
[14] Naito K.: On controllability for a nonlinear Volterra equation.Nonlinear Anal. 18 (1992), 99–108 Zbl 0768.93011, MR 1138645, 10.1016/0362-546X(92)90050-O |
| Reference:
|
[15] Pazy A.: Semigroups of Linear Operators and Applications to Partial Differential Equations.Springer–Verlag, New York 1983 Zbl 0516.47023, MR 0710486 |
| Reference:
|
[16] Showalter R. E.: A nonlinear parabolic Sobolev equation.J. Math. Anal. Appl. 50 (1975), 183–190 Zbl 0296.35047, MR 0361479, 10.1016/0022-247X(75)90047-5 |
| Reference:
|
[17] Triggiani R.: Controllability and observability in Banach space with bounded operators.SIAM J. Control 13 (1975), 462–491 MR 0394386, 10.1137/0313028 |
| Reference:
|
[18] Ward J. R.: Boundary value problems for differential equations in Banach spaces.J. Math. Anal. Appl. 70 (1979), 589–598 MR 0543596, 10.1016/0022-247X(79)90067-2 |
| . |
