Geodesic
Well-posedness and spectral analysis of integrodifferential equations arising in viscoelasticity theory
Contemporary Mathematics. Fundamental Directions, Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22–29, 2014). Part 1, Tome 58 (2015), pp. 22-42

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We study the well-posedness of initial-value problems for abstract integrodifferential equations with unbounded operator coefficients in Hilbert spaces and provide a spectral analysis of operator functions that are symbols of the specified equations. These equations represent an abstract form of linear partial integrodifferential equations arising in viscoelasticity theory and other important applications. For the said integrodifferential equations, we obtain well-posedness results in weighted Sobolev spaces of vector functions defined on the positive semiaxis and valued in a Hilbert space. For the symbols of the said equations, we find the localization and the structure of the spectrum. 
@article{CMFD_2015_58_a1,
     author = {V. V. Vlasov and N. A. Rautian},
     title = {Well-posedness and spectral analysis of integrodifferential equations arising in viscoelasticity theory},
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     volume = {58},
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     url = {http://geodesic.mathdoc.fr/item/CMFD_2015_58_a1/}
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V. V. Vlasov; N. A. Rautian. Well-posedness and spectral analysis of integrodifferential equations arising in viscoelasticity theory. Contemporary Mathematics. Fundamental Directions, Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22–29, 2014). Part 1, Tome 58 (2015), pp. 22-42. http://geodesic.mathdoc.fr/item/CMFD_2015_58_a1/