Geodesic
Degenerated integro-differential equations of special kind in Banach spaces and it's applications
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, no. 7 (2011), pp. 100-110 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper a special class of degenerated linear integro-differential equations in Banach spaces is investigated by the methods of the theory of fundamental operator-functions of singular integro-differential operators. Sufficient conditions of existence and uniqueness of Cauchy problem of classical solution are obtained. Abstract results are illustrated by two initial boundary value problems, arised in mathematical theory of viscoelasticity.
Keywords: Banach spaces, a fundamental operator-function.
Mots-clés : distributions 
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     title = {Degenerated integro-differential equations of special kind in {Banach} spaces and it's applications},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
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M. V. Falaleev; S. S. Orlov. Degenerated integro-differential equations of special kind in Banach spaces and it's applications. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, no. 7 (2011), pp. 100-110. http://geodesic.mathdoc.fr/item/VYURU_2011_7_a13/

[1] M. V. Falaleev, S. S. Orlov, “Nachalno-kraevye zadachi dlya integro-differentsialnykh uravnenii vyazkouprugosti”, Obozrenie prikladnoi i promyshlennoi matematiki, 17:4 (2010), 597–600

[2] G. A. Sviridyuk, V. E. Fedorov, Linear Sobolev Type Equations and Degenerate Semigroups of Operators, VSP, Utrecht–Boston–Köln–Tokyo, 2003 | MR | Zbl

[3] G. A. Sviridyuk, “K obschei teorii polugrupp operatorov”, Uspekhi mat. nauk, 49:4 (1994), 47–74 | MR | Zbl

[4] N. Sidorov, B. Loginov, A. Sinitsyn, M. Falaleev, Lyapunov–Schmidt Methods in Nonlinear Analysis and Applications, Kluwer Acad. Publ., Dordrecht, 2002 | MR | Zbl

[5] M. V. Falaleev, E. Yu. Grazhdantseva, “Fundamentalnye operator-funktsii singulyarnykh differentsialnykh operatorov v usloviyakh spektralnoi ogranichennosti”, Differents. uravneniya, 42:6 (2006), 769–774 | MR | Zbl

[6] M. V. Falaleev, “Fundamentalnye operator-funktsii singulyarnykh differentsialnykh operatorov v usloviyakh sektorialnosti i radialnosti”, Izvestiya vuzov. Matematika, 2006, no. 10, 68–75

[7] M. M. Cavalcanti, V. N. Domingos Cavalcanti, J. Ferreira, “Existence and Uniform Decay for a Non-Linear Viscoelastic Equation with Strong Damping”, Math. Meth. Appl. Sci., 24 (2001), 1043–1053 | DOI | MR | Zbl

[8] A. A. Zamyshlyaeva, “Fazovye prostranstva odnogo klassa lineinykh uravnenii sobolevskogo tipa vtorogo poryadka”, Vychislit. tekhnologii, 8:4 (2003), 45–54 | MR