Abstract
In this article, global asymptotic stability of solutions of non-homogeneous differential-operator equations of the third order is studied. It is proved that every solution of the equations decays exponentially under the Routh–Hurwitz criterion for the third order equations.
Article PDF
Similar content being viewed by others
References
Iovanovich, B.S.; Lemeshevski, S.V.; Matus, P.P.: Global stability of second-order operator-differential equations and three-layer operator-difference schemes. Dokl. Nats. Akad. Nauk Belarusi 46(4), 30–34 (2002). 124
Kalantarov, V.K.; Yilmaz, Y.: Decay and growth estimates for solutions of second-order and third-order differential-operator equations. Nonlinear Anal. 89, 1–7 (2013)
Quintanilla, R.; Racke, R.: A note on stability in three-phase-lag heat con- duction. Int. J. Heat and Mass Transf. 51, 24–29 (2008)
Kalantarov, V.K.; Tiryaki, A.: On the stability results for third-order differential-operator equations. Turk. J. Math. 21, 179–186 (1997)
Ladyzhenskaya, O.A.: On non-stationary operational equations and their applications to linear problems of mathematical physics. Mat. Sb. 45, 123–149 (1985)
Temam, R.: Infinite-dimensional dynamical systems in mechanics and physics. Applied Mathematical Sciences, vol. 68. Springer, New York (1997)
Tzou, D.Y.: The generalized lagging response in small-scale and high-rate heating. Int. J. Heat Mass Transf. 38(17), 3231–3240 (1995)
Varlamov, V.V.; Nesterov, A.V.: Asymptotic representation of the solution of the problem of the propagation of acoustic waves in a non-uniform compressible relaxing medium. USSR Comput. Math. Math. Phys. 30(3), 47–55 (1990)
Marchand, R.; McDevitt, T.; Triggiani, R.: An abstract semigroup approach to the third-order Moore–Gibson–Thompson partial differential equation arising in high-intensity ultrasound: structural decomposition, spectral analysis, exponential stability. Math. Methods Appl. Sci. 35(15), 1896–1929 (2012)
Remili, M.; Beldjerd, D.: Stability and ultimate boundedness of solutions of some third order differential equations with delay. J Assoc. Arab Univ. Basic Appl. Sci. 23, 90–95 (2017)
Graef, J.R.; Tunç, C.: Global asymptotic stability and boundedness of certain multi-delay functional differential equations of third order. Math. Methods Appl. Sci. 38(17), 3747–3752 (2015)
Tunç, C.: On the qualitative behaviors of nonlinear functional differential systems of third order. Advances in nonlinear analysis via the concept of measure of noncompactness, 421–439. Springer, Singapore (2017)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Yilmaz, Y., Kosal, I.A. & Bakankus, Y.E. Asymptotic stability for third-order non-homogeneous differential-operator equations. Arab. J. Math. 9, 223–229 (2020). https://doi.org/10.1007/s40065-018-0225-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40065-018-0225-5