Skip to main content
SpringerLink
Log in

Existence and Uniqueness of Solutions of SPDEs in Infinite Dimensions

  • Chapter
  • First Online:
Optimization, Control, and Applications of Stochastic Systems

Part of the book series: Systems & Control: Foundations & Applications ((SCFA))

  • 1371 Accesses

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Ahmed, N.U.: Semigroup Theory with Applications to Systems and Control, Pitman Research Notes in Math., Vol. 246, (1991).

    Google Scholar 

  2. Da Prato, G., Zabczyk, J.: Stochastic Equations in Infinite Dimensions, Cambridge Univ. Press, Cambridge, (1992).

    Book  MATH  Google Scholar 

  3. Da Prato, G., Zabczyk, J.: A note on stochastic convolution, Stochastic Anal. Appl. 10, 143–153 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  4. Govindan, T.E.: Almost sure exponential stability for stochastic neutral partial functional differential equations, Stochastics 77, 139–154 (2005).

    MathSciNet  MATH  Google Scholar 

  5. Govindan, T.E.: A new iteration procedure for stochastic neutral partial functional differential equations, Internat. J. Pure Applied Math. 56, 285–298 (2009).

    MathSciNet  MATH  Google Scholar 

  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. Hernandez, E., Henriquez, H.R.: Existence results for partial neutral functional differential equations with unbounded delay, J. Math. Anal. Appl. 221, 452–475 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  8. Luo, L.: Exponential stability for stochastic neutral partial functional differential equations, J. Math. Anal. Appl. 355, 414–425 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  9. Pazy, A.: Semigroups of Linear operators and Applications to Partial Differential Equations, Springer, New York, (1983).

    Book  MATH  Google Scholar 

  10. Taniguchi, T.: Asymptotic stability theorems of semilinear stochastic evolution equations in Hilbert spaces, Stochastics Stochastics Reports 53, 41–52 (1995).

    MATH  Google Scholar 

Download references

Acknowledgements

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

Author information

Authors and Affiliations

  1. ESFM, Instituto Politécnico Nacional, México D.F., 07738, México

    T. E. Govindan

Authors
  1. T. E. Govindan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. E. Govindan .

Editor information

Editors and Affiliations

  1. , Department of Probability and Statistics, Center for Research in Mathematics, Jalisco s/n, Guanajuato, 36000, Mexico

    Daniel Hernández-Hernández

  2. , Department of Mathematics, University of Sonora, Rosales s/n, Hermosillo, 83000, Sonora, Mexico

    J. Adolfo Minjárez-Sosa

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Govindan, T.E. (2012). Existence and Uniqueness of Solutions of SPDEs in Infinite Dimensions. In: Hernández-Hernández, D., Minjárez-Sosa, J. (eds) Optimization, Control, and Applications of Stochastic Systems. Systems & Control: Foundations & Applications. Birkhäuser, Boston. https://doi.org/10.1007/978-0-8176-8337-5_7

Download citation

Publish with us

Policies and ethics

Search

Navigation