About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 797516, 18 pages
http://dx.doi.org/10.1155/2012/797516
Research Article

Regularity for Variational Evolution Integrodifferential Inequalities

1Institute of Liberal Education, Catholic University of Daegu, Daegue 712-702, Republic of Korea
2Department of Applied Mathematics, Pukyong National University, Busan 608-737, Republic of Korea

Received 8 May 2012; Accepted 28 June 2012

Academic Editor: Sergey Piskarev

Copyright © 2012 Yong Han Kang and Jin-Mun Jeong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Nordhoff Leiden, The Netherlands, 1976. View at Zentralblatt MATH
  2. V. Barbu, Analysis and Control of Nonlinear Infinite Dimensional Systems, vol. 190 of Mathematics in Science and Engineering, Academic Press, Boston, Mass, USA, 1993. View at Zentralblatt MATH
  3. J.-M. Jeong, D.-H. Jeong, and J.-Y. Park, “Nonlinear variational evolution inequalities in Hilbert spaces,” International Journal of Mathematics and Mathematical Sciences, vol. 23, no. 1, pp. 11–20, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. N. U. Ahmed and X. Xiang, “Existence of solutions for a class of nonlinear evolution equations with nonmonotone perturbations,” Nonlinear Analysis. Series A, vol. 22, no. 1, pp. 81–89, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. J.-M. Jeong and J.-Y. Park, “Nonlinear variational inequalities of semilinear parabolic type,” Journal of Inequalities and Applications, vol. 6, no. 2, Article ID 896837, pp. 227–245, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. J. M. Jeong, Y. C. Kwun, and J. Y. Park, “Approximate controllability for semilinear retarded functional-differential equations,” Journal of Dynamical and Control Systems, vol. 5, no. 3, pp. 329–346, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. Y. Kobayashi, T. Matsumoto, and N. Tanaka, “Semigroups of locally Lipschitz operators associated with semilinear evolution equations,” Journal of Mathematical Analysis and Applications, vol. 330, no. 2, pp. 1042–1067, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. N. U. Ahmed, “Optimal control of infinite-dimensional systems governed by integrodifferential equations,” in Differential Equations, Dynamical Systems, and Control Science, vol. 152 of Lecture Notes in Pure and Applied Mathematics, pp. 383–402, Dekker, New York, NY, USA, 1994.
  9. H. Tanabe, Equations of Evolution, vol. 6 of Monographs and Studies in Mathematics, Pitman, London, UK, 1979.
  10. J. L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problmes and Applications, Springer, Berlin, Germany, 1972.
  11. H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, vol. 18 of North-Holland Mathematical Library, North-Holland, Amsterdam, The Netherlands, 1978.
  12. G. Di Blasio, K. Kunisch, and E. Sinestrari, “L2-regularity for parabolic partial integro-differential equations with delay in the highest-order derivatives,” Journal of Mathematical Analysis and Applications, vol. 102, no. 1, pp. 38–57, 1984. View at Publisher · View at Google Scholar
  13. J. L. Lions and E. Magenes, Problemes Aux Limites Non Homogenes Et Applications, vol. 3, Dunod, Paris, France, 1968.
  14. J. P. Aubin, “Un Théorème de Compacité,” Comptes Rendus de l'Académie des Sciences, vol. 256, pp. 5042–5044, 1963. View at Zentralblatt MATH