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Controllability for semilinear retarded control systems in Hilbert spaces. (English) Zbl 1139.35015
The authors consider a class of semilinear retarded functional differential equations. After proving well-posedness of the problem and \(L^2\)-regularity properties of the solutions, they establish a relation between the reachable set of a semilinear system and that of the corresponding linear system.

MSC:
35B37 PDE in connection with control problems (MSC2000)
35F25 Initial value problems for nonlinear first-order PDEs
35R10 Partial functional-differential equations
93B05 Controllability
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[1] J. P. Dauer and N. I. Mahmudov, Approximate controllability of semilinear functional equations in Hilbert spaces. J. Math. Anal. Appl. 273 (2002), 310–327. · Zbl 1017.93019
[2] G. Di Blasio, K. Kunisch, and E. Sinestrari, L 2-Regularity for parabolic partial integrodifferential equations with delay in the highest-order derivatives. J. Math. Anal. Appl. 102 (1984), 38–57. · Zbl 0538.45007
[3] J. M. Jeong, Y. C. Kwun, and J. Y. Park, Approximate controllability for semilinear retarded functional differential equations. J. Dynam. Control Systems 5 (1999), No. 3, 329–346. · Zbl 0962.93013
[4] K. Naito, Controllability of semilinear control systems dominated by the linear part. SIAM J. Control Optim. 25 (1987), 715–722. · Zbl 0617.93004
[5] N. Sukavanam and Nutan Kumar Tomar, Approximate controllability of semilinear delay control system. Nonlinear Func. Anal. Appl. (to appear). · Zbl 1141.93016
[6] H. Triebel, Interpolation theory, function spaces, differential operators. North-Holland (1978). · Zbl 0387.46032
[7] H. Tanabe, Equations of evolution. Pitman, London (1979). · Zbl 0417.35003
[8] _____, Fundamental solutions of differential equation with time delay in Banach space, Funkcial. Ekvac. 35 (1992), 149–177. · Zbl 0771.34060
[9] M. Yamamoto and J. Y. Park, Controllability for parabolic equations with uniformly bounded nonlinear terms, J. Optim. Theory Appl. 66 (1990), 515–532. · Zbl 0682.93012
[10] H. X. Zhou, Approximate controllability for a class of semilinear abstract equations. SIAM J. Control Optim. 21 (1983). · Zbl 0516.93009
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