Jeong, Jin-Mun; Kim, Jin-Ran; Roh, Hyun-Hee Controllability for semilinear retarded control systems in Hilbert spaces. (English) Zbl 1139.35015 J. Dyn. Control Syst. 13, No. 4, 577-591 (2007). 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. Reviewer: Gheorghe Aniculăesei (Iaşi) Cited in 11 Documents 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 Keywords:well-posedness; reachable set PDFBibTeX XMLCite \textit{J.-M. Jeong} et al., J. Dyn. Control Syst. 13, No. 4, 577--591 (2007; Zbl 1139.35015) Full Text: DOI References: [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 · doi:10.1016/S0022-247X(02)00225-1 [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 · doi:10.1016/0022-247X(84)90200-2 [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 · doi:10.1023/A:1021714500075 [4] K. Naito, Controllability of semilinear control systems dominated by the linear part. SIAM J. Control Optim. 25 (1987), 715–722. · Zbl 0617.93004 · doi:10.1137/0325040 [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 · doi:10.1007/BF00940936 [10] H. X. Zhou, Approximate controllability for a class of semilinear abstract equations. SIAM J. Control Optim. 21 (1983). · Zbl 0516.93009 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.