Geodesic
Linear Models in Theory of Viscoelasticity of Sobolev Type
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 6 (2013) no. 4, pp. 101-107 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper the Cauchy problem for integral differential equation in Banach spaces of a Sobolev type is analyzed by the methods of fundamental operator-functions theory and the theory of operator semigroups with kernels. Fundamental operator-function is constructed and with its help constructive formulae for generalized solution in class of distributions with left-bounded support are obtained. Equal conditions for generalized and classical solutions are described. Abstract results are illustrated by Cauchy–Dirichle problems arised in mathematical theory of viscoelasticity.
Keywords: Banach spaces; generalized functions; viscoelasticity. 
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     title = {Linear {Models} in {Theory} of {Viscoelasticity} of {Sobolev} {Type}},
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M. V. Falaleev. Linear Models in Theory of Viscoelasticity of Sobolev Type. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 6 (2013) no. 4, pp. 101-107. http://geodesic.mathdoc.fr/item/VYURU_2013_6_4_a9/

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

[2] Sviridyuk G. A., “On the General Theory of Operator Semigroups”, Russ. Math. Surv., 49:4 (1994), 47–74 | MR | Zbl

[3] Falaleev M. V., “Integro-Differential Equations with Fredholm Operator by the Derivative of the Higest Order in Banach Spaces and It's Applications”, J. News of Irkutsk State University. Series «Mathematics», 5:2 (2012), 90–102 | Zbl

[4] 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

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