Existence and Uniqueness of Solutions of SPDEs in Infinite Dimensions

  • T. E. GovindanEmail author
Part of the Systems & Control: Foundations & Applications book series (SCFA)


This chapter concerns neutral stochastic partial differential equations (SPDEs) in infinite dimensions. The goal here is to investigate the existence and uniqueness of a mild solution of SPDEs by using the semigroup theory and some properties of a stochastic convolution integral. Two examples are provided to illustrate the theory.


Bounded Linear Operator Mild Solution Infinitesimal Generator Analytic Semigroup Stochastic Partial Differential Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The author wishes to thank SIP and COFAA both from IPN, Mexico for financial support.


  1. 1.
    Ahmed, N.U.: Semigroup Theory with Applications to Systems and Control, Pitman Research Notes in Math., Vol. 246, (1991).Google Scholar
  2. 2.
    Da Prato, G., Zabczyk, J.: Stochastic Equations in Infinite Dimensions, Cambridge Univ. Press, Cambridge, (1992).zbMATHCrossRefGoogle Scholar
  3. 3.
    Da Prato, G., Zabczyk, J.: A note on stochastic convolution, Stochastic Anal. Appl. 10, 143–153 (1992).MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Govindan, T.E.: Almost sure exponential stability for stochastic neutral partial functional differential equations, Stochastics 77, 139–154 (2005).MathSciNetzbMATHGoogle Scholar
  5. 5.
    Govindan, T.E.: A new iteration procedure for stochastic neutral partial functional differential equations, Internat. J. Pure Applied Math. 56, 285–298 (2009).MathSciNetzbMATHGoogle Scholar
  6. 6.
    Govindan, T.E.: Mild solutions of neutral stochastic partial functional differential equations, Internat. J. Stochastic Anal. vol. 2011, Article ID 186206, 13 pages, (2011). doi:10.1155/2011/186206.Google Scholar
  7. 7.
    Hernandez, E., Henriquez, H.R.: Existence results for partial neutral functional differential equations with unbounded delay, J. Math. Anal. Appl. 221, 452–475 (1998).MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Luo, L.: Exponential stability for stochastic neutral partial functional differential equations, J. Math. Anal. Appl. 355, 414–425 (2009).MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Pazy, A.: Semigroups of Linear operators and Applications to Partial Differential Equations, Springer, New York, (1983).zbMATHCrossRefGoogle Scholar
  10. 10.
    Taniguchi, T.: Asymptotic stability theorems of semilinear stochastic evolution equations in Hilbert spaces, Stochastics Stochastics Reports 53, 41–52 (1995).zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.ESFM, Instituto Politécnico NacionalMéxico D.F.México

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