Skip to main content

Attractors for a Random Evolution Equation with Infinite Memory: An Application

  • Chapter
  • First Online:
Modern Mathematics and Mechanics

Abstract

In this paper we study the existence of random pullback attractors for an integro-differential parabolic equation of reaction-diffusion type with both finite and infinite delays and also some kind of randomness.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 199.99
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

Similar content being viewed by others

References

  1. Arnold, L.: Random Dynamical Systems. Springer Monographs in Mathematics. Springer, Berlin (1998)

    Google Scholar 

  2. Caraballo, T., Chueshov, I.D., Real, J.: Pullback attractors for stochastic heat equations in materials with memory. Discrete Contin. Dyn. Syst. Ser. B 9, 525–539 (2008)

    Article  MathSciNet  Google Scholar 

  3. Caraballo, T., Garrido-Atienza, M.J., Schmalfuss, B., Valero, J.: Asymptotic behaviour of a stochastic semilineardissipative functional equation without uniqueness of solutions. Discrete Contin. Dyn. Syst. Ser. B 14, 439–455 (2010)

    Article  MathSciNet  Google Scholar 

  4. Caraballo, T., Garrido-Atienza, M.J., Schmalfuss, B., Valero, J.: Attractors for a random evolution equation with infinite memory: theoretical results. Discrete Contin. Dyn. Syst. Ser. B 22, 1779–1800 (2017)

    Article  MathSciNet  Google Scholar 

  5. Castaing, C., Valadier, M.: Convex Analysis and Measurable Multifunctions. Springer, Berlin (1977)

    Book  Google Scholar 

  6. Chueshov, I.D., Scheutzow, M.: Inertial manifolds and forms for stochastically perturbed retarded semilinear parabolic equations. J. Dyn. Differ. Equ. 13, 355–380 (2001)

    Article  MathSciNet  Google Scholar 

  7. Hino, Y., Murakami, S., Naito, T.: Functional Differential Equations with Infinite Delay. Lecture Notes in Mathematics, vol. 1473. Springer, Berlin (1991)

    Google Scholar 

  8. Lions, J.L.: Quelques méthodes de résolution des problèmes aux limites non linéaires. Gauthier-Villar, Paris (1969)

    MATH  Google Scholar 

  9. Robinson, J.: Infinite-Dimensional Dynamical Systems. Cambridge University Press, Cambridge (2001)

    Book  Google Scholar 

  10. Yosida, K.: Functional Analysis. Springer, Berlin (1965).

    MATH  Google Scholar 

Download references

Acknowledgements

This work has been partially supported by Spanish Ministry of Economy and Competitiveness and FEDER, projects MTM2015-63723-P and MTM2016-74921-P, and by Junta de Andalucía (Spain), project P12-FQM-1492.

We would like to thank the referees for their valuable remarks and suggestions.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to José Valero .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Garrido-Atienza, M.J., Schmalfuß, B., Valero, J. (2019). Attractors for a Random Evolution Equation with Infinite Memory: An Application. In: Sadovnichiy, V., Zgurovsky, M. (eds) Modern Mathematics and Mechanics. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-96755-4_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-96755-4_13

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-96754-7

  • Online ISBN: 978-3-319-96755-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics