Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

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)
  • Received : 2010.03.10
  • Published : 2012.09.01
Download PDF
⟨ Previous Next ⟩

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

References

  1. J. P. Aubin, Un theoreme de compasite, C. R. Acad. Sci. 256 (1963), 5042-5044.
  2. V. Barbu, Nonlinear Semigroups and Differential Equations in Banach space, Nordhoff Leiden, Netherland, 1976.
  3. V. Barbu, Analysis and Control of Nonlinear In nite Dimensional Systems, Academic Press Limited, 1993.
  4. 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. https://doi.org/10.1016/0022-247X(84)90200-2
  5. P. L. Butzer and H. Berens, Semi-Groups of Operators and Approximation, Springer-verlag, Belin-Heidelberg-Newyork, 1967.
  6. 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. https://doi.org/10.1023/A:1021714500075
  7. J. M. Jeong and H. H. Roh, Approximate controllability for semilinear retarded systems, J. Math. Anal. Appl. 321 (2006), no. 2, 961-975. https://doi.org/10.1016/j.jmaa.2005.09.005
  8. J. L. Lions and E. Magenes, Problema aux limites non homogenes et applications, vol. 3, Dunod, Paris, 1968.
  9. K. Naito, Controllability of semilinear control systems dominated by the linear part, SIAM J. Control Optim. 25 (1987), no. 3, 715-722. https://doi.org/10.1137/0325040
  10. H. Tanabe, Equations of Evolution, Pitman-London, 1979.
  11. H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North- Holland, 1978.