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http://dx.doi.org/10.4134/JKMS.2012.49.5.881

CONTROLLABILITY FOR NONLINEAR VARIATIONAL EVOLUTION INEQUALITIES  

Park, Jong-Yeoul (Department of Mathematics Pusan National University)
Jeong, Jin-Mun (Department of Applied Mathematics Pukyong National University)
Rho, Hyun-Hee (Department of Mathematics Pukyong National University)
Publication Information
Journal of the Korean Mathematical Society / v.49, no.5, 2012 , pp. 881-891 More about this Journal
Abstract
In this paper we investigate the approximate controllability for the following nonlinear functional differential control problem: $$x^{\prime}(t)+Ax(t)+{\partial}{\phi}(x(t)){\ni}f(t,x(t))+h(t)$$ which is governed by the variational inequality problem with nonlinear terms.
Keywords
approximate controllability; variational inequality; subdifferential operator; degree theory;
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1 G. Di Blasio, K. Kunisch, and E. Sinestrari, $L^{2}$-regularity for parabolic partial integro- differential equations with delay in the highest-order derivatives, J. Math. Anal. Appl. 102 (1984), no. 1, 38-57.   DOI   ScienceOn
2 P. L. Butzer and H. Berens, Semi-Groups of Operators and Approximation, Springer-verlag, Belin-Heidelberg-Newyork, 1967.
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.   DOI
4 J. M. Jeong and H. H. Roh, Approximate controllability for semilinear retarded systems, J. Math. Anal. Appl. 321 (2006), no. 2, 961-975.   DOI   ScienceOn
5 J. L. Lions and E. Magenes, Problema aux limites non homogenes et applications, vol. 3, Dunod, Paris, 1968.
6 K. Naito, Controllability of semilinear control systems dominated by the linear part, SIAM J. Control Optim. 25 (1987), no. 3, 715-722.   DOI   ScienceOn
7 H. Tanabe, Equations of Evolution, Pitman-London, 1979.
8 H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North- Holland, 1978.
9 V. Barbu, Nonlinear Semigroups and Differential Equations in Banach space, Nordhoff Leiden, Netherland, 1976.
10 J. P. Aubin, Un theoreme de compasite, C. R. Acad. Sci. 256 (1963), 5042-5044.
11 V. Barbu, Analysis and Control of Nonlinear In nite Dimensional Systems, Academic Press Limited, 1993.