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On the Absolute Exponential Stability of Solutions of Systems of Linear Parabolic Differential Equations with One Delay

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Nonlinear Oscillations

Abstract

We investigate necessary conditions for the absolute exponential stability of a system of linear parabolic differential equations with one delay.

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References

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

    Google Scholar 

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

    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 Divergent Argument [in Russian], No. 7, 219-292 (1992).

    Google Scholar 

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

    Google Scholar 

  5. V. E. Slyusarchuk, “Absolute exponential stability of linear differential equations of the neutral type in a Banach space,” Differents. Uravn., 16, No. 3, 462-469 (1980).

    Google Scholar 

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

    Google Scholar 

  7. 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).

    Google Scholar 

  8. V. E. Slyusarchuk, “Absolute asymptotic stability of linear differential equations with an infinite number of delays in a Banach space,” Differents. Uravn., 12, No. 5, 840-847 (1976).

    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).

    Google Scholar 

  10. D. Henry, Geometric Theory of Semilinear Parabolic Equations, Springer, Berlin (1981).

    Google Scholar 

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

    Google Scholar 

  12. V. P. Kushnir, “On the stabilization of solutions of partial differential equations with delays,” in: Boundary-Value Problems for Differential Equations [in Ukrainian], Issue 1, 116-125 (1998).

    Google Scholar 

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Authors and Affiliations

  1. Ukrainian State University of Water Management, Rivn

    V. P. Kushnir

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  1. V. P. Kushnir
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Kushnir, V.P. On the Absolute Exponential Stability of Solutions of Systems of Linear Parabolic Differential Equations with One Delay. Nonlinear Oscillations 6, 50–53 (2003). https://doi.org/10.1023/A:1024871503542

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