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Around Ovsyannikov's method

Dmitri Finkelshtein Orcid Logo

Methods of Functional Analysis and Topology, Volume: 21, Issue: 2, Pages: 134 - 150

Swansea University Author: Dmitri Finkelshtein Orcid Logo

Abstract

We study existence, uniqueness, and a limiting behaviour 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 $C_0$...

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Published in: Methods of Functional Analysis and Topology
Published: 2015
Online Access: http://www.imath.kiev.ua/~mfat/
URI: https://cronfa.swan.ac.uk/Record/cronfa22265
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Abstract: We study existence, uniqueness, and a limiting behaviour 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 $C_0$-semigroup acting in each of the spaces of the scale. The results are (slightly modified) abstract version of those considered in [D. Finkelshtein, Y. Kondratiev, Y. Kozitsky, O.Kutoviy. The statistical dynamics of a spatial logistic model and the related kinetic equation. Math. Models Methods Appl. Sci., 25 (2): 343-370, 2015] for a particular equation. An application to a birth-and-death stochastic dynamics in the continuum is considered.
Keywords: Ovsyannikov's method, scale of spaces, evolution equations, birth-and-death dynamics, Vlasov scaling, kinetic equation
College: Faculty of Science and Engineering
Issue: 2
Start Page: 134
End Page: 150