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

Full Text

Article Information

Title	Around Ovsyannikov's method
Source	Methods Funct. Anal. Topology, Vol. 21 (2015), no. 2, 134–150
MathSciNet	3407906
zbMATH	06533472
Milestones	Received 20/01/2015
Copyright	The 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

Citation Example

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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