Asymptotics of the Multidimensional Nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov Equation Near a Quasistationary Solution

Abstract

Asymptotic solutions of the multidimensional nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation with an influence function that is invariant with respect to a spatial shift are constructed. The asymptotic solutions are perturbations of a spatially-homogeneous quasistationary exact solution. General expressions are illustrated by the example of a two-dimensional equation with a Gaussian initial condition.

Original language	English
Journal	Russian Physics Journal
DOIs	https://doi.org/10.1007/s11182-015-0594-6
Publication status	Accepted/In press - 16 Nov 2015

Keywords

asymptotic solutions
multidimensional nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation
quasistationary solution

ASJC Scopus subject areas

Physics and Astronomy(all)

Access to Document

10.1007/s11182-015-0594-6

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title = "Asymptotics of the Multidimensional Nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov Equation Near a Quasistationary Solution",

abstract = "Asymptotic solutions of the multidimensional nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation with an influence function that is invariant with respect to a spatial shift are constructed. The asymptotic solutions are perturbations of a spatially-homogeneous quasistationary exact solution. General expressions are illustrated by the example of a two-dimensional equation with a Gaussian initial condition.",

keywords = "asymptotic solutions, multidimensional nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation, quasistationary solution",

author = "Levchenko, {Evgeniy Anatolievich} and Trifonov, {A. Y.} and Shapovalov, {Aleksandr Vasilievich}",

year = "2015",

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day = "16",

doi = "10.1007/s11182-015-0594-6",

language = "English",

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AU - Levchenko, Evgeniy Anatolievich

AU - Trifonov, A. Y.

AU - Shapovalov, Aleksandr Vasilievich

PY - 2015/11/16

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N2 - Asymptotic solutions of the multidimensional nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation with an influence function that is invariant with respect to a spatial shift are constructed. The asymptotic solutions are perturbations of a spatially-homogeneous quasistationary exact solution. General expressions are illustrated by the example of a two-dimensional equation with a Gaussian initial condition.

AB - Asymptotic solutions of the multidimensional nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation with an influence function that is invariant with respect to a spatial shift are constructed. The asymptotic solutions are perturbations of a spatially-homogeneous quasistationary exact solution. General expressions are illustrated by the example of a two-dimensional equation with a Gaussian initial condition.

KW - asymptotic solutions

KW - multidimensional nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation

KW - quasistationary solution

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