Study of functional-differential equations with unbounded operator coefficients
- Authors: Vlasov V.V.1, Rautian N.A.1
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Affiliations:
- Faculty of Mechanics and Mathematics
- Issue: Vol 96, No 3 (2017)
- Pages: 620-624
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225433
- DOI: https://doi.org/10.1134/S1064562417060291
- ID: 225433
Cite item
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.
About the authors
V. V. Vlasov
Faculty of Mechanics and Mathematics
Author for correspondence.
Email: vikmont@yandex.ru
Russian Federation, Moscow, 119992
N. A. Rautian
Faculty of Mechanics and Mathematics
Email: vikmont@yandex.ru
Russian Federation, Moscow, 119992