Journal article 1245 views
Around Ovsyannikov's method
Dmitri Finkelshtein 
Methods of Functional Analysis and Topology, Volume: 21, Issue: 2, Pages: 134 - 150
Swansea University Author:
Dmitri Finkelshtein
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 $C_0$...
| Published in: | Methods of Functional Analysis and Topology |
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| Published: |
2015
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| 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. |
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| 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 |