About this Journal Submit a Manuscript Table of Contents
International Journal of Stochastic Analysis
Volume 2011 (2011), Article ID 186206, 13 pages
http://dx.doi.org/10.1155/2011/186206
Research Article

Mild Solutions of Neutral Stochastic Partial Functional Differential Equations

Departamento de Matemáticas, ESFM, Instituto Politécnico Nacional, 07738 México, DF, Mexico

Received 28 December 2010; Revised 8 May 2011; Accepted 7 June 2011

Academic Editor: V. V. Anh

Copyright © 2011 T. E. Govindan. 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. T. E. Govindan, “Almost sure exponential stability for stochastic neutral partial functional differential equations,” Stochastics, vol. 77, no. 2, pp. 139–154, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. T. Taniguchi, K. Liu, and A. Truman, “Existence, uniqueness, and asymptotic behavior of mild solutions to stochastic functional differential equations in Hilbert spaces,” Journal of Differential Equations, vol. 181, no. 1, pp. 72–91, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. T. E. Govindan, “Stability properties in the α-norm of solutions of stochastic partial functional differential equations,” Differential and Integral Equations, vol. 23, no. 5-6, pp. 401–418, 2010.
  4. T. E. Govindan, “A new iteration procedure for stochastic neutral partial functional differential equations,” International Journal of Pure and Applied Mathematics, vol. 56, no. 2, pp. 285–298, 2009. View at Zentralblatt MATH
  5. M. Adimy and K. Ezzinbi, “Existence and stability in the α-norm for partial functional differential equations of neutral type,” Annali di Matematica Pura ed Applicata, vol. 185, no. 3, pp. 437–460, 2006. View at Publisher · View at Google Scholar
  6. J. Wu, Theory and Applications of Partial Functional Differential Equations, Springer-Verlag, New York, NY, USA, 1996.
  7. K. Ezzinbi, X. Fu, and K. Hilal, “Existence and regularity in the α-norm for some neutral partial differential equations with nonlocal conditions,” Nonlinear Analysis, vol. 67, no. 5, pp. 1613–1622, 2007. View at Publisher · View at Google Scholar
  8. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, NY, USA, 1983.
  9. N. U. Ahmed, Semigroup Theory with Applications to Systems and Control, vol. 246 of Pitman Research Notes in Mathematics Series, Longman Scientific and Technical, Harlow, UK, 1991.
  10. T. E. Govindan, “Autonomous semilinear stochastic Volterra integrodifferential equations in Hilbert spaces,” Dynamic Systems and Applications, vol. 3, no. 1, pp. 51–74, 1994. View at Zentralblatt MATH
  11. G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, vol. 44, Cambridge University Press, Cambridge, UK, 1992.