Публікація: Around Ovsyannikov's method
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Автори
Finkelshtein, Dmitri
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Анотація
We study existence, uniqueness, and a limiting behavior of solutions to an abstract linear evolution equation in a scale of Banach spaces. The generator of the equation is a perturbation of the operator which satisfies the classical assumptions of Ovsyannikov’s method by a generator of a C0-semigroup acting in each of the spaces of the scale. The results are (slightly modified) abstract version of those considered in [10] for a particular equation. An application to a birth-and-death stochastic dynamics in the continuum is considered.
Опис
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Ovsyannikov’s method, scale of spaces, evolution equations, birth-and-death dynamics, Vlasov scaling, kinetic equation
Бібліографічний опис
Finkelshtein, D. Around Ovsyannikov's method / D. Finkelshtein // Methods of Functional Analysis and Topology : Quarterly journal. – 2015. - Vol. 21, № 2. - pp. 134-150.