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

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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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     author = {M. V. Falaleev},
     title = {Linear {Models} in {Theory} of {Viscoelasticity} of {Sobolev} {Type}},
     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. 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/