Linear Models in Theory of Viscoelasticity of Sobolev Type
Abstract
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.
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