Skip to main content
SpringerLink
Log in

Exponential stability of Itô-type evolution differential equations of first and second order

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

The exponential stability of evolution differential equations obtained on the basis of heat conduction equations is studied. To determine the boundaries of stochastic stability of the solution of these equations, we use the method of construction of a Lyapunov functional.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ya. S. Podstrigach and Yu. M. Kolyano, Generalized Thermomechanics [in Russian], Naukova Dumka, Kiev (1976).

  2. J. Appleby, X. Mao, and A. Rodkina, “On stabilization of differential equations,” Discrete Contin. Dyn. Syst. Ser. A, 15, No. 3, 843–857 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  3. T. Caraballo, “Asymptotic exponential stability of stochastic partial differential equations with delay,” Stochastics, 33, 27–47 (1990).

    MathSciNet  MATH  Google Scholar 

  4. T. Caraballo, “On the pathwise exponential stability of non-linear stochastic partial differential equations,” Stoch. Anal. Appl., 12, 517–525 (1994).

    Article  MathSciNet  MATH  Google Scholar 

  5. T. Caraballo and K. Liu, “On exponential stability criteria of stochastic partial equation,” Stoch. Proc. Appl., 83, 289–301 (1999).

    Article  MathSciNet  MATH  Google Scholar 

  6. P. L. Chow, “Stability of non-linear stochastic evolution equations,” J. Math. Anal. Appl., 89, 400–419 (1982).

    Article  MathSciNet  MATH  Google Scholar 

  7. U. G. Haussmann, “Asymptotic stability of the linear Itô equation in infinite dimensional,” J. Math. Anal. Appl., 65, 219–235 (1978).

    Article  MathSciNet  MATH  Google Scholar 

  8. A. Ichikawa, “Stability of semilinear stochastic evolution equations,” J. Math. Anal. Appl., 90, 12–44 (1982).

    Article  MathSciNet  MATH  Google Scholar 

  9. X. R. Mao, Exponential Stability of Stochastic Differential Equations, Marcel Dekker, New York (1994).

    MATH  Google Scholar 

  10. X. R. Mao, Stochastic Differential Equations and Applications, Horwood, New York (2007).

    MATH  Google Scholar 

  11. A. Pardoux, Équations aux Dérivées Partielles Stochastiques Non Linéaires Monotones, Thèse, Université Paris-Sud XI, Paris (1975).

Download references

Author information

Authors and Affiliations

  1. Politechnika Rzeszówska, Rzeszów, Poland

    M. Król

Authors
  1. M. Król
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 52, No. 4, pp. 99–107, October–December, 2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Król, M. Exponential stability of Itô-type evolution differential equations of first and second order. J Math Sci 174, 243–253 (2011). https://doi.org/10.1007/s10958-011-0294-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-011-0294-x

Keywords

Search

Navigation