Skip to main content
SpringerLink
Log in

Absolute asymptotic stability of solutions of linear parabolic differential equations with delay

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We establish necessary and sufficient conditions for the absolute asymptotic stability of solutions of linear parabolic differential equations with delay.

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

References

  1. L. É. Él’sgol’ts and S. B. Norkin, Introduction to the Theory of Differential Equations with Deviating Argument [in Russian], Nauka, Moscow (1971).

    MATH  Google Scholar 

  2. R. Bellman and K. L. Cooke, Differential-Difference Equations, Academic Press, New York (1963).

    MATH  Google Scholar 

  3. L. A. Zhivotovskii, “Absolute stability of solutions of differential equations with several delays,” in: Proceedings of the Seminar on the Theory of Differential Equations with Deviating Argument, No. 7 (1969), pp. 219–292.

  4. Yu. M. Repin, “On conditions for stability of systems of linear differential equations for any delays,” Uch. Zap. Ural. Univ., 23, 31–34 (1960).

    Google Scholar 

  5. D. H. Korenivs’kyi, “On some criteria for stability of linear stationary systems with delay,” Dopov. Akad. Nauk Ukr. SSR, No. 6, 708–710 (1966).

    Google Scholar 

  6. D. G. Korenevskii, “Algebraic coefficient criteria for absolute (independent of delay) asymptotic stability of solutions of systems of linear differential equations with aftereffect,” Mat. Fiz. Nelin. Mekh., Issue 7, 5–9 (1987).

  7. V. E. Slyusarchuk, “Necessary and sufficient conditions for the absolute exponential stability of solutions of linear scalar differential equations of neutral type,” in: Problems of Contemporary Theory of Periodic Motion [in Russian], No. 6 (1982), pp. 19–24.

  8. V. E. Slyusarchuk, “Sufficient conditions for the absolute asymptotic stability of linear differential equations in a Banach space with several delays,” Mat. Zametki, 17, No. 6, 919–923 (1975).

    MATH  MathSciNet  Google Scholar 

  9. V. E. Slyusarchuk, “Necessary and sufficient conditions for the absolute exponential stability of solutions of differential equations of delay and neutral types,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 12, 17–19 (1983).

  10. S. G. Mikhlin, A Course of Mathematical Physics [in Russian], Nauka, Moscow (1968).

    Google Scholar 

  11. V. P. Kushnir, “On stabilization of solutions of linear parabolic differential equations with delay,” in: Integral Transformations and Their Application to Boundary-Value Problems [in Ukrainian], Issue 15 (1997), pp. 111–119.

  12. V. P. Kushnir, “Absolute exponential stability of solutions of linear parabolic differential equations with delay,” Nelin. Kolyvannya, 5, No. 2, 170–178 (2002).

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National University of Water Management and Nature Resources Application, Rivne, Ukraine

    V. P. Kushnir

Authors
  1. V. P. Kushnir
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 12, pp. 1714–1721, December, 2007.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kushnir, V.P. Absolute asymptotic stability of solutions of linear parabolic differential equations with delay. Ukr Math J 59, 1932–1941 (2007). https://doi.org/10.1007/s11253-008-0036-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-008-0036-5

Keywords

Search

Navigation