Evolution of initial distributions with one and two centers in a two-dimensional model of the reaction-diffusion type with a nonlocal interaction of finite radius

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Abstract

Solutions of a generalized Fisher-Kolmogorov-Petrovskii-Piskunov equation for a nonlocal interaction of finite radius have been constructed for initial conditions with one and two localization centers by using numerical methods. The dynamics depends on the choice of the equation parameters and initial conditions. The processes of formation and interaction of the rings expanding from each of the two localization centers and the formation of dissipative structures are considered.

Original languageEnglish
Pages (from-to)32-38
Number of pages7
JournalRussian Physics Journal
Volume54
Issue number1
DOIs
Publication statusPublished - Jun 2011

Fingerprint

two dimensional models
radii
interactions
rings

Keywords

  • bacterial colonies
  • dissipative structures
  • equations of the "reaction-diffusion" type

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

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title = "Evolution of initial distributions with one and two centers in a two-dimensional model of the reaction-diffusion type with a nonlocal interaction of finite radius",
abstract = "Solutions of a generalized Fisher-Kolmogorov-Petrovskii-Piskunov equation for a nonlocal interaction of finite radius have been constructed for initial conditions with one and two localization centers by using numerical methods. The dynamics depends on the choice of the equation parameters and initial conditions. The processes of formation and interaction of the rings expanding from each of the two localization centers and the formation of dissipative structures are considered.",
keywords = "bacterial colonies, dissipative structures, equations of the {"}reaction-diffusion{"} type",
author = "Borisov, {A. V.} and Trifonov, {A. Yu} and Shapovalov, {Aleksandr Vasilievich}",
year = "2011",
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doi = "10.1007/s11182-011-9575-6",
language = "English",
volume = "54",
pages = "32--38",
journal = "Russian Physics Journal",
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T1 - Evolution of initial distributions with one and two centers in a two-dimensional model of the reaction-diffusion type with a nonlocal interaction of finite radius

AU - Borisov, A. V.

AU - Trifonov, A. Yu

AU - Shapovalov, Aleksandr Vasilievich

PY - 2011/6

Y1 - 2011/6

N2 - Solutions of a generalized Fisher-Kolmogorov-Petrovskii-Piskunov equation for a nonlocal interaction of finite radius have been constructed for initial conditions with one and two localization centers by using numerical methods. The dynamics depends on the choice of the equation parameters and initial conditions. The processes of formation and interaction of the rings expanding from each of the two localization centers and the formation of dissipative structures are considered.

AB - Solutions of a generalized Fisher-Kolmogorov-Petrovskii-Piskunov equation for a nonlocal interaction of finite radius have been constructed for initial conditions with one and two localization centers by using numerical methods. The dynamics depends on the choice of the equation parameters and initial conditions. The processes of formation and interaction of the rings expanding from each of the two localization centers and the formation of dissipative structures are considered.

KW - bacterial colonies

KW - dissipative structures

KW - equations of the "reaction-diffusion" type

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JO - Russian Physics Journal

JF - Russian Physics Journal

SN - 1064-8887

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