Abstract
We study the well-posed solvability of initial value problems for abstract integrodifferential equations with unbounded operator coefficients in a Hilbert space. These equations are an abstract form of linear partial integro-differential equations that arise in the theory of viscoelasticity and have a series of other important applications. We obtain results on the wellposed solvability of the considered integro-differential equations in weighted Sobolev spaces of vector functions defined on the positive half-line and ranging in a Hilbert space.
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Original Russian Text © V.V. Vlasov, N.A. Rautian, 2016, published in Differentsial’nye Uravneniya, 2016, Vol. 52, No. 9, pp. 1168–1177.
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Vlasov, V.V., Rautian, N.A. Well-posed solvability of volterra integro-differential equations in Hilbert space. Diff Equat 52, 1123–1132 (2016). https://doi.org/10.1134/S0012266116090032
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DOI: https://doi.org/10.1134/S0012266116090032