Geodesic
Controllability of functional differential systems of Sobolev type in Banach spaces
Kybernetika, Tome 34 (1998) no. 3, pp. 349-357 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 34G20, 93B05, 93C25
Keywords: controllability; Banach space; differential system of Sobolev type 
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     title = {Controllability of functional differential systems of {Sobolev} type in {Banach} spaces},
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Balachandran, Krishnan; Dauer, Jerald P. Controllability of functional differential systems of Sobolev type in Banach spaces. Kybernetika, Tome 34 (1998) no. 3, pp. 349-357. http://geodesic.mathdoc.fr/item/KYB_1998_34_3_a6/

[1] Balachandran K., Balasubramaniam P., Dauer J. P.: Controllability of nonlinear integrodifferential systems in Banach space. J. Optim. Theory Appl. 84 (1995), 83–91 | DOI | MR | Zbl

[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

[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 | DOI | MR

[4] Brill H.: A semilinear Sobolev equation in Banach space. J. Differential Equations 24 (1977), 412–425 | DOI | MR

[5] Chuckwu E. N., Lenhart S. M.: Controllability questions for nonlinear systems in abstract spaces. J. Optim. Theory Appl. 68 (1991), 437–462 | DOI | MR

[6] Curtain R. F., Prichard A. J.: Infinite Dimensional Linear Systems Theory. Springer–Verlag, New York 1978 | MR

[7] Kartsatos A. C., Parrott M. E.: On a class of nonlinear functional pseudoparabolic problems. Funkcial. Ekvac. 25 (1982), 207–221 | MR | Zbl

[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

[9] Lagnese J.: General boundary value problems for differential equations of Sobolov type. SIAM J. Math. Anal. 3 (1972) 105–119 | DOI | MR

[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 | DOI | MR

[11] Lightbourne J. H., Rankin S. M.: A partial functional differential equation of Sobolev type. J. Math. Anal. Appl. 93 (1983), 328–337 | DOI | MR | Zbl

[12] Nakagiri S., Yamamoto R.: Controllability and observability of linear retarded systems in Banach spaces. Internat. J. Control 49 (1989), 1489–1504 | DOI | MR | Zbl

[13] Naito K.: Approximate controllability for trajectories of semilinear control systems. J. Optim. Theory Appl. 6 (1989), 57–65 | DOI | MR | Zbl

[14] Naito K.: On controllability for a nonlinear Volterra equation. Nonlinear Anal. 18 (1992), 99–108 | DOI | MR | Zbl

[15] Pazy A.: Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer–Verlag, New York 1983 | MR | Zbl

[16] Showalter R. E.: A nonlinear parabolic Sobolev equation. J. Math. Anal. Appl. 50 (1975), 183–190 | DOI | MR | Zbl

[17] Triggiani R.: Controllability and observability in Banach space with bounded operators. SIAM J. Control 13 (1975), 462–491 | DOI | MR

[18] Ward J. R.: Boundary value problems for differential equations in Banach spaces. J. Math. Anal. Appl. 70 (1979), 589–598 | DOI | MR