Elementary particle physics and field theory: Asymptotic behavior of the one-dimensional fisher–kolmogorov–petrovskii–piskunov equation with anomalouos diffusion

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Abstract

Asymptotic solutions of the nonlocal, one-dimensional Fisher–Kolmogorov–Petrovskii–Piskunov equation with fractional derivatives in the diffusion operator are constructed. The fractional derivative is defined in accordance with the approaches of Weyl, Grünwald–Letnilkov, and Liouville. Asymptotic solutions are constructed in a class of functions that are a perturbation of the found exact quasistationary solution and tend at large times to this quasistationary solution. It is shown that the presence of fractional derivatives leads to drift of the center of mass of the initial distribution and breaks its symmetry.

Original languageEnglish
Article numberA019
Pages (from-to)399-409
Number of pages11
JournalRussian Physics Journal
Volume58
Issue number3
DOIs
Publication statusPublished - 17 Jul 2015

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elementary particles
physics
center of mass
operators
perturbation
symmetry

Keywords

  • Anomalous diffusion
  • Asymmetric solutions
  • Nonlocal Fisher–KPP equation

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

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title = "Elementary particle physics and field theory: Asymptotic behavior of the one-dimensional fisher–kolmogorov–petrovskii–piskunov equation with anomalouos diffusion",
abstract = "Asymptotic solutions of the nonlocal, one-dimensional Fisher–Kolmogorov–Petrovskii–Piskunov equation with fractional derivatives in the diffusion operator are constructed. The fractional derivative is defined in accordance with the approaches of Weyl, Gr{\"u}nwald–Letnilkov, and Liouville. Asymptotic solutions are constructed in a class of functions that are a perturbation of the found exact quasistationary solution and tend at large times to this quasistationary solution. It is shown that the presence of fractional derivatives leads to drift of the center of mass of the initial distribution and breaks its symmetry.",
keywords = "Anomalous diffusion, Asymmetric solutions, Nonlocal Fisher–KPP equation",
author = "Prozorov, {Alexander Andreevich} and Trifonov, {A. Yu} and Shapovalov, {Aleksandr Vasilievich}",
year = "2015",
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T2 - Asymptotic behavior of the one-dimensional fisher–kolmogorov–petrovskii–piskunov equation with anomalouos diffusion

AU - Prozorov, Alexander Andreevich

AU - Trifonov, A. Yu

AU - Shapovalov, Aleksandr Vasilievich

PY - 2015/7/17

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N2 - Asymptotic solutions of the nonlocal, one-dimensional Fisher–Kolmogorov–Petrovskii–Piskunov equation with fractional derivatives in the diffusion operator are constructed. The fractional derivative is defined in accordance with the approaches of Weyl, Grünwald–Letnilkov, and Liouville. Asymptotic solutions are constructed in a class of functions that are a perturbation of the found exact quasistationary solution and tend at large times to this quasistationary solution. It is shown that the presence of fractional derivatives leads to drift of the center of mass of the initial distribution and breaks its symmetry.

AB - Asymptotic solutions of the nonlocal, one-dimensional Fisher–Kolmogorov–Petrovskii–Piskunov equation with fractional derivatives in the diffusion operator are constructed. The fractional derivative is defined in accordance with the approaches of Weyl, Grünwald–Letnilkov, and Liouville. Asymptotic solutions are constructed in a class of functions that are a perturbation of the found exact quasistationary solution and tend at large times to this quasistationary solution. It is shown that the presence of fractional derivatives leads to drift of the center of mass of the initial distribution and breaks its symmetry.

KW - Anomalous diffusion

KW - Asymmetric solutions

KW - Nonlocal Fisher–KPP equation

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