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Mat. Zametki, 2018, Volume 103, Issue 5, Pages 702–719 (Mi mz11703)  

This article is cited in 4 scientific papers (total in 4 papers)

Exponential Stability of a Certain Semigroup and Applications

D. A. Zakoraab

a Voronezh State University
b Crimea Federal University, Simferopol

Abstract: The uniform exponential stability of a $C_0$-semigroup with generator of a special form is proved. Such semigroups arise in the study of various problems of the theory of viscoelasticity. The proved statement is applied to the study of the asymptotic behavior of solutions in the problem of small motions of a viscoelastic body subject to driving forces of a special form.

Keywords: $C_0$-semigroup, integro-differential equation, exponential stability, materials with memory, asymptotics.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 14.Z50.31.0037
This work was supported by the Ministry of Education and Science of the Russian Federation (grant no. 14.Z50.31.0037).


DOI: https://doi.org/10.4213/mzm11703

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English version:
Mathematical Notes, 2018, 103:5, 745–760

Bibliographic databases:

UDC: 517.968.72
Received: 29.05.2017

Citation: D. A. Zakora, “Exponential Stability of a Certain Semigroup and Applications”, Mat. Zametki, 103:5 (2018), 702–719; Math. Notes, 103:5 (2018), 745–760

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. A. Zakora, “Asimptotika reshenii sistemy svyazannykh integro-differentsialnykh nepolnykh operatornykh uravnenii vtorogo poryadka”, Sib. elektron. matem. izv., 15 (2018), 971–986  mathnet  crossref
    2. D. A. Zakora, “Operatornyi podkhod k zadache o malykh dvizheniyakh idealnoi relaksiruyuschei zhidkosti”, Trudy Krymskoi osennei matematicheskoi shkoly-simpoziuma, SMFN, 64, no. 3, Rossiiskii universitet druzhby narodov, M., 2018, 459–489  mathnet  crossref
    3. D. A. Zakora, “Asymptotics of solutions in the problem about small motions of a compressible Maxwell fluid”, Differ. Equ., 55:9 (2019), 1150–1163  crossref  mathscinet  zmath  isi
    4. Yu. A. Tikhonov, “Analyticity of an operator semigroup arising in viscoelasticity problems”, Differ. Equ., 56:6 (2020), 797–812  crossref  mathscinet  zmath  isi
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