Open Access

Kawasaki dynamics in the continuum via generating functionals evolution

Abstract

We construct the time evolution of Kawasaki dynamics for a spatial infinite particle system in terms of generating functionals. This is carried out by an Ovsjannikov-type result in a scale of Banach spaces, which leads to a local (in time) solution. An application of this approach to Vlasov-type scaling in terms of generating functionals is considered as well.

Key words: Generating functional, Kawasaki dynamics, interacting particle system, continuous system, Ovsjannikov’s method, Vlasov scaling.

Article Information

 Title Kawasaki dynamics in the continuum via generating functionals evolution Source Methods Funct. Anal. Topology, Vol. 18 (2012), no. 1, 55-67 MathSciNet MR2953330 zbMATH 1249.82007 Copyright The Author(s) 2012 (CC BY-SA)

Authors Information

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

Yu. G. Kondratiev
Fakultat fur Mathematik, Universitat Bielefeld, D 33615 Bielefeld, Germany; Forschungszentrum BiBoS, Universitat Bielefeld, D 33615 Bielefeld, Germany

M. J. Oliveira
Universidade Aberta, P 1269-001 Lisbon, Portugal; CMAF, University of Lisbon, P 1649-003 Lisbon, Portugal

Citation Example

D. L. Finkelshtein, Yu. G. Kondratiev, and M. J. Oliveira, Kawasaki dynamics in the continuum via generating functionals evolution, Methods Funct. Anal. Topology 18 (2012), no. 1, 55-67.

BibTex

@article {MFAT605,
AUTHOR = {Finkelshtein, D. L. and Kondratiev, Yu. G. and Oliveira, M. J.},
TITLE = {Kawasaki dynamics in the continuum via generating functionals evolution},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {18},
YEAR = {2012},
NUMBER = {1},
PAGES = {55-67},
ISSN = {1029-3531},
MRNUMBER = {MR2953330},
ZBLNUMBER = {1249.82007},
URL = {http://mfat.imath.kiev.ua/article/?id=605},
}