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- Title
Study of functional-differential equations with unbounded operator coefficients.
- Authors
Vlasov, V.; Rautian, N.
- Abstract
Functional-differential and integro-differential equations with the principal part being an abstract hyperbolic equation perturbed by terms with unbounded variable operator coefficients multiplying variable delays are studied. Additionally, Volterra integral operators are considered. For the equations under study, the well-posedness of initial value problems in Sobolev spaces of vector functions is proved. In the autonomous case, spectral analysis of the operator functions that are the symbols of the indicated equations is performed.
- Subjects
INTEGRO-differential equations; SOBOLEV gradients; SOBOLEV spaces; NUMERICAL solutions to Voterra equations; VOLTERRA operators
- Publication
Doklady Mathematics, 2017, Vol 96, Issue 3, p620
- ISSN
1064-5624
- Publication type
Article
- DOI
10.1134/S1064562417060291