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| Content Provider | Springer Nature Link |
|---|---|
| Author | Fedorov, V. E. Borel, L. V. |
| Copyright Year | 2016 |
| 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 (C $_{0}$)-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. |
| Starting Page | 704 |
| Ending Page | 714 |
| Page Count | 11 |
| File Format | |
| ISSN | 00374466 |
| Journal | Siberian Mathematical Journal |
| Volume Number | 57 |
| Issue Number | 4 |
| e-ISSN | 15739260 |
| Language | English |
| Publisher | Pleiades Publishing |
| Publisher Date | 2016-08-23 |
| Publisher Place | Moscow |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | evolution equation operator semigroup equation with memory integrodifferential equation initial-boundary value problem Kelvin–Voigt fluid Mathematics |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
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