zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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.
35B37PDE in connection with control problems (MSC2000)
35F25Initial value problems for first order nonlinear PDE
35R10Partial functional-differential equations
[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).
[6]H. Triebel, Interpolation theory, function spaces, differential operators. North-Holland (1978).
[7]H. Tanabe, Equations of evolution. Pitman, London (1979).
[8]_____, Fundamental solutions of differential equation with time delay in Banach space, Funkcial. Ekvac. 35 (1992), 149–177.
[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).