Taiwanese Journal of Mathematics

Controllability for Nonlinear Variational Inequalities of Parabolic Type

Jin-Mun Jeong, Eun Young Ju, and Kyeong Yeon Lee

Full-text: Open access

PDF File (110 KB)

Abstract

This paper deal with the approximate controllability for the nonlinear functional differential control problem governed by the variational inequality. Sufficient conditions for the approximate controllability of the system are discussed under the bounded condition on the controller operator independent of the the time interval. We also prove the regularity and norm estimations for solutions of the given problems.

Article information

Source
Taiwanese J. Math., Volume 15, Number 2 (2011), 857-873.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406238

Digital Object Identifier
doi:10.11650/twjm/1500406238

Mathematical Reviews number (MathSciNet)
MR2810185

Zentralblatt MATH identifier
1229.93020

Subjects
Primary: 93C20: Systems governed by partial differential equations
Secondary: 49J40: Variational methods including variational inequalities [See also 47J20]

Keywords
approximate controllability regularity parabolic variational inequalities subdifferential operator

Citation

Jeong, Jin-Mun; Ju, Eun Young; Lee, Kyeong Yeon. Controllability for Nonlinear Variational Inequalities of Parabolic Type. Taiwanese J. Math. 15 (2011), no. 2, 857--873. doi:10.11650/twjm/1500406238. https://projecteuclid.org/euclid.twjm/1500406238


Export citation

References

  • J. P. Aubin, Un théorème de compacité, C. R. Acad. Sci., 256 (1963), 5042-5044.
  • H. Brézis, Opérateurs Maximaux Monotones et Semigroupes de Contractions dans un Espace de Hilbert, North Holland, 1973.
  • V. Barbu, Analysis and Control of Nonlinear Infinite Dimensional Systems, Academic Press Limited, 1993.
    Zentralblatt MATH: 0776.49005
  • V. Barbu, Nonlinear Semigroups and Differential Equations in Banach space, Nordhoff Leiden, Netherlands, 1976.
    Zentralblatt MATH: 0328.47035
  • 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.
    Zentralblatt MATH: 0538.45007
    Digital Object Identifier: doi:10.1016/0022-247X(84)90200-2
  • P. L. Butzer and H. Berens, Semigroup of Operators and Approximation, Springer-Verlag Berlin Heidelberg New York, 1967.
    Zentralblatt MATH: 0164.43702
  • A. Carrasco and H. Lebia, Approximate controllability of a system of parabolic equations with delay, J. Math. Anal. Appl., 345 (2008), 845-853.
    Zentralblatt MATH: 1140.93012
    Digital Object Identifier: doi:10.1016/j.jmaa.2008.04.068
  • J. M. Jeong, Retarded functional differential equations with $L^1$-valued controller, Funkcial. Ekvac., 36 (1993), 71-93.
    Mathematical Reviews (MathSciNet): MR1232080
    Zentralblatt MATH: 0791.35140
  • J. M. Jeong and J. Y. Park, Nonlinear variational inequalities of semilinear parabolic type, J. Inequal. & Appl., 6 (2001), 227-245.
    Zentralblatt MATH: 1032.35116
  • J. L. Lions and E. Magenes, Problèma aux limites non homogènes et applications, Vol. 3, Dunod, Paris, 1968.
  • N. I. Mahmudov, Approximate controllability of evolution systems with nonlocal conditions, Nonlinear Analysis, 68 (2008), 536-546.
    Zentralblatt MATH: 1129.93004
    Digital Object Identifier: doi:10.1016/j.na.2006.11.018
  • K. Naito, Controllability of semilinear control systems dominated by the linear part, SIAM J. Control and Optimization, 25 (1987), 715-722.
    Mathematical Reviews (MathSciNet): MR885194
    Zentralblatt MATH: 0617.93004
    Digital Object Identifier: doi:10.1137/0325040
  • R. Sakthivel, N. I. Mahmudov and J. H. Kim, Approximate controllability of nonlinear impulsive differential systems, Rep. Math. Phys., 60 (2007), 85-96.
    Mathematical Reviews (MathSciNet): MR2355467
    Zentralblatt MATH: 1141.93015
    Digital Object Identifier: doi:10.1016/S0034-4877(07)80100-5
  • H. Tanabe, Equations of Evolution, Pitman-London, 1979.
    Zentralblatt MATH: 0417.35003
  • H. X. Zhou, Approximate controllability for a class of semilinear abstract equations, SIAM J. Control and Optimization, 21(4) (1983), 551-556.
    Zentralblatt MATH: 0516.93009
    Digital Object Identifier: doi:10.1137/0321033

Mathematical Society of the Republic of China

Taiwanese Journal of Mathematics

New content alerts

Email RSS ToC RSS Article
  • You have access to this content.
  • You have partial access to this content.
  • You do not have access to this content.
Turn Off MathJax

What is MathJax?

More like this

+ See more