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- Title
Well-posed solvability of volterra integro-differential equations in Hilbert space.
- Authors
Vlasov, V.; Rautian, N.
- 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.
- Subjects
NUMERICAL solutions to Voterra equations; NUMERICAL solutions to integro-differential equations; HILBERT space; NUMERICAL solutions to initial value problems; OPERATOR theory
- Publication
Differential Equations, 2016, Vol 52, Issue 9, p1123
- ISSN
0012-2661
- Publication type
Article
- DOI
10.1134/S0012266116090032