Local controllability of quasilinear integrodifferential evolution systems in Banach spaces

Journal of Mathematical Analysis and Applications

Volumn 258, Issue 1, 2001, Pages 309-319

  Balachandran, K ^a   Park, J Y ^b   Anandhi, E R ^a  

^a BHARATHIAR UNIVERSITY   (India)

^b Pusan National University   (South Korea)

Author keywords

Controllability, quasilinear integrodifferential system, analytic semigroup, fixed point theorem

Indexed keywords

EID: 0042418621     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.2000.7388     Document Type: Article

References (27)

1. Bahuguna D. Quasilinear integrodifferential equations in Banach spaces. Nonlinear Anal. Theory Methods Appl. 24:1995;175-183.
2. Balachandran K., Dauer J. P. Local controllability of semilinear evolution systems in Banach Spaces. Indian J. Pure Appl. Math. 29:1998;311-320.
3. Balachandran K., Balasubramaniam P., Dauer J. P. Controllability of quasilinear delay systems in Banach Spaces. Optim. Control Appl. Methods. 16:1995;283-290.
4. Balachandran K., Dauer J. P., Balasubramaniam P. Local null controllability of nonlinear functional differential systems in Banach Spaces. J. Optim. Theory Appl. 88:1996;61-75.
5. Bian W. M. Controllability of nonlinear evolution systems with preassigned responses. J. Optim. Theory Appl. 100:1999;265-285.
6. Chukwu E. N., Lenhart S. M. Controllability questions for nonlinear systems in abstract spaces. J. Optim. Theory Appl. 68:1991;437-462.
7. Curtain R. F., Zwart H. An Introduction to Infinite Dimensional Linear Systems Theory. 1995;Springer-Verlag, Berlin.
8. Do V. N. A note on approximate controllability of semilinear systems. Systems Control Lett. 12:1989;365-371.
9. Friedman A. Partial Differential Equations. 1969;Holt, Rinehart, and Winston, NewYork.
10. Heard M. L. A quasilinear hyperbolic integrodifferential equation related to a nonlinear string. Trans. Amer. Math. Soc. 285:1984;805-823.
11. Kato T. Quasilinear equations of evolution with application to partial differential equations. Lecture Notes in Math. 448:1978;25-70.
12. 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.
13. Klamka J. Constrained controllability of nonlinear systems. J. Math. Anal. Appl. 201:1996;365-374.
14. Naito K. Controllability of semilinear control systems dominated by the linear part. SIAM J. Control Optim. 25:1987;715-722.
15. Naito K. Approximate controllability for trajectories of semilinear control systems. J. Optim. Theory Appl. 60:1989;57-65.
16. Naito K. On controllability for a nonlinear Volterra equation. Nonlinear Anal. Theory Methods Appl. 18:1992;99-108.
17. Narasimha R. Nonlinear vibration of an elastic string. J. Sound Vibration. 8:1968;134-146.
18. Oka H. Abstract quasilinear Volterra integrodiffrential equations. Nonlinear Anal. Theory Methods Appl. 28:1997;1019-1045.
19. Oka H., Tanaka N. Abstract quasilinear integrodifferential equations of hyperbolic type. Nonlinear Anal. Theory Methods Appl. 29:1997;903-925.
20. Oplinger D. W. Frequency response of a nonlinear stretched string. J. Acoustic Soc. Amer. 32:1960;1529-1538.
21. Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations. 1983;Springer-Verlag, New York.
22. Peichl G., Schappacher W. Constrained controllability in Banach spaces. SIAM J. Control Optim. 24:1986;1261-1275.
23. Quinn M. D., Carmichael N. An approach to nonlinear control problems using fixed point methods, degree theory, and pseudo-inverses. Numer. Funct. Anal. Optim. 7:1984/1985;197-219.
24. Sobolevskii P. E. Equations of parabolic type in Banach spaces. Amer. Math. Soc. Transl. 49:1965;1-62.
25. Yamamoto M., Park J. Y. Controllability for parabolic equations with uniformly bounded nonlinear terms. J. Optim. Theory Appl. 66:1990;515-532.
26. Zhou H. X. Approximate controllability for a class of semilinear abstract equations. SIAM J. Control Optim. 21:1983;551-565.
27. Zhou H. X. Controllability properties of linear and semilinear abstract control systems. SIAM J. Control Optim. 22:1984;405-422.