Study of degenerate evolution equations with memory by operator semigroup methods
- Authors: Fedorov V.E.1, Borel L.V.1
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Affiliations:
- Chelyabinsk State University
- Issue: Vol 57, No 4 (2016)
- Pages: 704-714
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/170627
- DOI: https://doi.org/10.1134/S0037446616040121
- ID: 170627
Cite item
Abstract
We reduce the problem with some history prescribed for an integrodifferential equation in a Banach space including memory effect to the Cauchy problem for some evolution system with a constant operator in a larger space that possesses a resolvent (C0)-semigroup. This enables us to state conditions for the existence of a unique classical solution to the original problem. We use the results to study the unique solvability of problems with history prescribed for degenerate linear evolution equations with memory in Banach spaces. We show that the initial-boundary value problem for the linearized integrodifferential Oskolkov system describing the dynamics of Kelvin–Voigt fluids in linear approximation belongs to this class of problems.
About the authors
V. E. Fedorov
Chelyabinsk State University
Author for correspondence.
Email: kar@csu.ru
Russian Federation, Chelyabinsk
L. V. Borel
Chelyabinsk State University
Email: kar@csu.ru
Russian Federation, Chelyabinsk