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Around Ovsyannikov's method


Abstract

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 $C_0$-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.

Key words: Ovsyannikov’s method, scale of spaces, evolution equations, birth-and-death dynamics, Vlasov scaling, kinetic equation


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Article Information

TitleAround Ovsyannikov's method
SourceMethods Funct. Anal. Topology, Vol. 21 (2015), no. 2, 134–150
MathSciNet 3407906
zbMATH 06533472
MilestonesReceived 20/01/2015
CopyrightThe Author(s) 2015 (CC BY-SA)

Authors Information

D. L. Finkelshtein
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine


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Dmitri Finkelshtein, Around Ovsyannikov's method, Methods Funct. Anal. Topology 21 (2015), no. 2, 134–150.


BibTex

@article {MFAT771,
    AUTHOR = {Finkelshtein, Dmitri},
     TITLE = {Around Ovsyannikov's method},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {21},
      YEAR = {2015},
    NUMBER = {2},
     PAGES = {134–150},
      ISSN = {1029-3531},
  MRNUMBER = {3407906},
 ZBLNUMBER = {06533472},
       URL = {http://mfat.imath.kiev.ua/article/?id=771},
}


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