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Mathematical notes of NEFU, 2016, Volume 23, Issue 4, Pages 58–72 (Mi svfu39)  

Mathematics

Resolving operators of a linear degenerate evolution equation with Caputo derivative. The sectorial case

E. A. Romanovaa, V. E. Fedorovab

a Chelyabinsk State University, Mathematical Analysis Department, 129 Kashirin Brothers Street, Chelyabinsk 454001, Russia;
b Shadrinsk State Pedagogical University, 3 Karl Liebknecht st7, Shadrinsk 641870, Kurgan reg.

Abstract: Unique solvability of the Cauchy problem for an equation in a Banach space with degenerate operator at the fractional Caputo derivative is studied. Previously found conditions of the existence of analytic in a sector resolving operators family for the equation with the degeneration on the kernel of the operator at the derivative is used. The form of the resolving operators is established. Under the satisfied conditions, the existence is shown for the unique solution of the Cauchy problem to the researched equation with initial data from the complement of the kernel of the operator at the derivative and the solution is presented using the resolving operators. The obtained results are applied to studying the linearized quasistationary time-fractional order system of the phase field equations.

Keywords: degenerate evolution equation, fractional Caputo derivative, analytic in a sector resolving operators family, Cauchy problem, initial boundary value problem, system of partial differential equations.

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Document Type: Article
UDC: 517.9
Received: 18.09.2016

Citation: E. A. Romanova, V. E. Fedorov, “Resolving operators of a linear degenerate evolution equation with Caputo derivative. The sectorial case”, Mathematical notes of NEFU, 23:4 (2016), 58–72

Citation in format AMSBIB
\Bibitem{RomFed16}
\by E.~A.~Romanova, V.~E.~Fedorov
\paper Resolving operators of a linear degenerate evolution equation with Caputo derivative. The sectorial case
\jour Mathematical notes of NEFU
\yr 2016
\vol 23
\issue 4
\pages 58--72
\mathnet{http://mi.mathnet.ru/svfu39}
\elib{http://elibrary.ru/item.asp?id=29959202}


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