Exact solutions in front propagation problems with superdiffusion

V. A. Volpert; Y. Nec; A. A. Nepomnyashchy

doi:10.1016/j.physd.2009.10.011

Exact solutions in front propagation problems with superdiffusion

V. A. Volpert^*, Y. Nec, A. A. Nepomnyashchy

^*Corresponding author for this work

Engineering Sciences and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

Abstract

Front propagation in a number of reaction-superdiffusion problems is studied. Specifically, traveling wave propagation, domain wall pinning, and systems of waves governed by a bistable single equation as well as FitzHugh-Nagumo equations are considered. The reaction terms in the equations are taken in the form of piecewise linear functions, which allow for exact solutions to be obtained. The effect of superdiffusion on front propagation is discussed.

Original language	English (US)
Pages (from-to)	134-144
Number of pages	11
Journal	Physica D: Nonlinear Phenomena
Volume	239
Issue number	3-4
DOIs	https://doi.org/10.1016/j.physd.2009.10.011
State	Published - Feb 2010

Keywords

Exact solution
FitzHugh-Nagumo equations
Front
Reaction-diffusion problem
Superdiffusion

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/j.physd.2009.10.011

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title = "Exact solutions in front propagation problems with superdiffusion",

abstract = "Front propagation in a number of reaction-superdiffusion problems is studied. Specifically, traveling wave propagation, domain wall pinning, and systems of waves governed by a bistable single equation as well as FitzHugh-Nagumo equations are considered. The reaction terms in the equations are taken in the form of piecewise linear functions, which allow for exact solutions to be obtained. The effect of superdiffusion on front propagation is discussed.",

keywords = "Exact solution, FitzHugh-Nagumo equations, Front, Reaction-diffusion problem, Superdiffusion",

author = "Volpert, {V. A.} and Y. Nec and Nepomnyashchy, {A. A.}",

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pages = "134--144",

journal = "Physica D: Nonlinear Phenomena",

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TY - JOUR

T1 - Exact solutions in front propagation problems with superdiffusion

AU - Volpert, V. A.

AU - Nec, Y.

AU - Nepomnyashchy, A. A.

PY - 2010/2

Y1 - 2010/2

N2 - Front propagation in a number of reaction-superdiffusion problems is studied. Specifically, traveling wave propagation, domain wall pinning, and systems of waves governed by a bistable single equation as well as FitzHugh-Nagumo equations are considered. The reaction terms in the equations are taken in the form of piecewise linear functions, which allow for exact solutions to be obtained. The effect of superdiffusion on front propagation is discussed.

AB - Front propagation in a number of reaction-superdiffusion problems is studied. Specifically, traveling wave propagation, domain wall pinning, and systems of waves governed by a bistable single equation as well as FitzHugh-Nagumo equations are considered. The reaction terms in the equations are taken in the form of piecewise linear functions, which allow for exact solutions to be obtained. The effect of superdiffusion on front propagation is discussed.

KW - Exact solution

KW - FitzHugh-Nagumo equations

KW - Front

KW - Reaction-diffusion problem

KW - Superdiffusion

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M3 - Article

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VL - 239

SP - 134

EP - 144

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 3-4

ER -

Exact solutions in front propagation problems with superdiffusion

Abstract

Keywords

ASJC Scopus subject areas

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