Browse > Article
http://dx.doi.org/10.5666/KMJ.2019.59.2.241

Null Controllability of Semilinear Integrodifferential Control Systems in Hilbert Spaces  

Park, Ah-ran (Department of Applied Mathematics, Pukyong National University)
Jeong, Jin-Mun (Department of Applied Mathematics, Pukyong National University)
Publication Information
Kyungpook Mathematical Journal / v.59, no.2, 2019 , pp. 241-258 More about this Journal
Abstract
In this paper, we deal with the null controllability of semilinear functional integrodifferential control systems under the Lipschitz continuity of nonlinear terms. Moreover, we establish the regularity and a variation of constant formula for solutions of the given control systems in Hilbert spaces.
Keywords
controllability; semilinear control system; regularity for solution; analytic semigroup; integrodifferential control system;
Citations & Related Records
연도 인용수 순위
  • Reference
1 J. P. Aubin, Un theoreme de compacite, C. R. Acad. Sci. Paris, 256(1963), 5042-5044.
2 K. Balachandran and J. P. Dauer, Controllability of nonlinear systems in Banach spaces: a survey, J. Optim. Theory Appl., 115(2002), 7-28.   DOI
3 V. Barbu, Nonlinear semigroups and differential equations in Banach spaces, Nordhoff Leiden, Netherlands, 1976.
4 G. Di Blasio, K. Kunisch and E. Sinestrari, $L^2$-regularity for parabolic partial in-tegrodifferential equations with delay in the highest-order derivatives, J. Math. Anal. Appl., 102(1984), 38-57.   DOI
5 P. L. Butzer and H. Berens, Semi-groups of operators and approximation, Springer-verlag, Belin-Heidelberg-Newyork, 1967.
6 A. Carrasco and H. Leiva, Approximate controllability of a system of parabolic equations with delay, J. Math. Anal. Appl., 345(2008), 845-853.   DOI
7 R. F. Curtain and H. Zwart, An introduction to infinite dimensional linear systems theory, Springer-Verlag, New York, 1995.
8 J. P. Dauer and N. I. Mahmudov, Exact null controllability of semilinear integro-differential systems in Hilbert spaces, J. Math. Anal. Appl., 299(2004), 322-332.   DOI
9 J. M. Jeong, Y. C. Kwun and J. Y. Park, Approximate controllability for semilinear retarded functional differential equations, J. Dynam. Control Systems, 5(3)(1999), 329-346.   DOI
10 J. M. Jeong and H. H. Roh, Approximate controllability for semilinear retarded systems, J. Math. Anal. Appl., 321(2006), 961-975.   DOI
11 J. M. Jeong, J. E. Ju and K. Y. Lee, Controllability for variational inequalities of parabolic type with nonlinear perturbation, J. Inequal. Appl., (2010), Art. ID 768469, 16 pp.
12 J. M. Jeong, J. R. Kim and H. G. Kim, Regularity for solutions of nonlinear second order evolution equations, J. Math. Anal. Appl., 338(2008), 209-222.   DOI
13 J. L. Lions, Quelques methodes de resolution des problems aux limites non-lineaires, Paris, Dunnod, Gauthier-Villars, 1969.
14 J. L. Lions and E. Magenes, Non-homogeneous boundary value problemes and applications, Springer-Verlag, Berlin-heidelberg-New York, 1972.
15 N. I. Mahmudov, Approximate controllability of evolution systems with nonlocal conditions, Nonlinear Anal., 68(2008), 536-546.   DOI
16 K. Naito, Controllability of semilinear control systems dominated by the linear part, SIAM J. Control Optim., 25(1987), 715-722.   DOI
17 D. G. Park, J. M. Jeong and S. H. Park, Regularity of parabolic hemivariational inequalities with boundary conditions, J. Inequal. Appl., (2009), Art. ID 207873, 22 pp.
18 J. Y. Park and S. H. Park, On solutions for a hyperbolic system with differential inclusion and memory source term on the boundary, Nonlinear Anal., 57(2004), 459-472.   DOI
19 R. Sakthivel, N. I. Mahmudov and J. H. Kim, Approximate controllability of nonlinear impulsive differential systems, Rep. Math. Phys., 60(2007), 85-96.   DOI
20 N. Sukavanam and N. K. Tomar, Approximate controllability of semilinear delay control systems, Nonlinear Funct. Anal. Appl., 12(2007), 53-59.
21 H. Tanabe, Equations of evolution, Pitman, Boston, Mass.-London, 1979.
22 H. Triebel, Interpolation theory, function spaces, differential operators, NorthHolland, 1978.
23 H. X. Zhou, Approximate controllability for a class of semilinear abstract equations, SIAM J. Control Optim., 21(1983), 551-565.   DOI