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References (31)
-
(1994)
Parabolic Volterra Equations of Convolution Type -
V. Vlasov, D. Medvedev (2010)
Functional-differential equations in Sobolev spaces and related problems of spectral theoryJournal of Mathematical Sciences, 164
-
G. Blasio, K. Kunisch, E. Sinestrari (1985)
Stability for abstract linear functional differential equationsIsrael Journal of Mathematics, 50
-
V.V. Vlasov (1995)
On the Solvability and Properties of Solutions of Functional-Differential Equations in a Hilbert SpaceMat. Sb., 186
-
(1970)
Osnovy matematicheskoi teorii termovyazkouprugosti (Foundations of the Mathematical Theory of Thermal Viscoelasticity) -
V.V. Vlasov, N.A. Rautian, A.S. Shamaev (2010)
Solvability and Spectral Analysis of Integro-Differential Equations That Arise in Thermophysics and AcousticsDokl. Akad. Nauk, 434
-
J.L. Lions, E. Magenes (1972)
Nonhomogeneous Boundary-Value Problems and Applications -
(1980)
Translated under the title Neodnorodnye sredy i teoriya kolebanii -
W. Desch, Richard Miller (1987)
Exponential stabilization of Volterra integrodifferential equations in Hilbert spaceJournal of Differential Equations, 70
-
Yu.N. Rabotnov (1977)
Elementy nasledstvennoi mekhaniki tverdykh tel -
(1999)
On the Solvability and Estimates for the Solutions of Functional-Differential Equations in Sobolev Spaces, Tr -
V.V. Vlasov, A.A. Gavrikov, S.A. Ivanov (2009)
Spectral Properties of Combined MediaSovrem. Probl. Mat. Mekh., 5
-
V.V. Vlasov, N.A. Rautian (2015)
Well-Posed Solvability and Spectral Analysis of Integro-Differential Equations That Arise in Theory of ViscoelasticitySovrem. Mat. Fundam. Napravl., 58
-
(2011)
Well-Defined Solvability and Spectral Analysis of Abstract Hyperbolic Equations -
(2003)
On Two-Scalar Convergence -
(2011)
Spectral Analysis and Well-Posed Solvability of Abstract Integro-Differential Equations That Arise in Thermophysics and Acoustics, Sovrem -
A.A. Il’yushin, B.E. Pobedrya (1970)
Osnovy matematicheskoi teorii termovyazkouprugosti -
(2009)
Spectral Properties of Combined Media, Sovrem -
L. Pandolfi (2005)
The Controllability of the Gurtin-Pipkin Equation: A Cosine Operator ApproachApplied Mathematics and Optimization, 52
-
E. Palencia (1980)
Non-Homogeneous Media and Vibration Theory -
R.K. Miller (1975)
Volterra Integral Equation in Banach SpaceFunkcial. Ekvac., 18
-
M. Gurtin, A. Pipkin (1968)
A general theory of heat conduction with finite wave speedsArchive for Rational Mechanics and Analysis, 31
-
Jianhong Wu (1996)
Theory and Applications of Partial Functional Differential Equations -
V. Vlasov, N. Rautian (2015)
Spectral analysis of hyperbolic Volterra integro-differential equationsDoklady Mathematics, 92
-
(1972)
Nonhomogeneous Boundary-Value Problems and Applications, Berlin -
(2000)
On an Extension and an Application of the Two-Scale Convergence Method -
(1976)
Problema teplo-i massoobmena -
V.V. Vlasov, N.A. Rautian (2014)
Properties of Solutions of Integro-Differential Equations Arising in Heat and Mass Transfer TheoryTr. Mosk. Mat. Obs., 75
-
V.V. Vlasov, N.A. Rautian (2015)
Spectral Analysis of Hyperbolic Volterra Integro-Differential EquationsDokl. Akad. Nauk, 464
-
Tosio Kato (1966)
Perturbation theory for linear operators -
V. Vlasov, N. Rautian (2014)
Properties of solutions of integro-differential equations arising in heat and mass transfer theoryTransactions of the Moscow Mathematical Society, 75
- Publisher
- Springer Journals
- Copyright
- Copyright © 2016 by Pleiades Publishing, Ltd.
- Subject
- Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
- ISSN
- 0012-2661
- eISSN
- 1608-3083
- DOI
- 10.1134/S0012266116090032
- Publisher site
- See Article on Publisher Site
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.
Journal
Differential Equations – Springer Journals
Published: Oct 19, 2016