Blowing-up solutions to systems of fractional differential and integral equations with exponential non-linearities

A. Kadem; M. Kirane; C. M. Kirk; W. E. Olmstead

doi:10.1093/imamat/hxt005

Blowing-up solutions to systems of fractional differential and integral equations with exponential non-linearities

A. Kadem, M. Kirane, C. M. Kirk^*, W. E. Olmstead

^*Corresponding author for this work

Engineering Sciences and Applied Mathematics

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

10 Scopus citations

Abstract

We consider two separate systems of fractional differential equations with exponential non-linearities. We also consider the corresponding systems of non-linear Volterra integral equations. We present results on the non-existence of global solutions for each system. Bounds on the blow-up time for each system are provided along with the asymptotic growth near blow-up. Each system can be regarded as a model for the interaction of two weakly diffusive media subjected to Arrhenius-type reactions. Our results indicate that a thermal blow-up cannot be avoided under such conditions.

Original language	English (US)
Pages (from-to)	1077-1088
Number of pages	12
Journal	IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Volume	79
Issue number	6
DOIs	https://doi.org/10.1093/imamat/hxt005
State	Published - Aug 5 2014

Keywords

anomalous diffusion
blow-up
fractional differential and integral equations
nonlinear Volterra equation

ASJC Scopus subject areas

Applied Mathematics

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10.1093/imamat/hxt005

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title = "Blowing-up solutions to systems of fractional differential and integral equations with exponential non-linearities",

abstract = "We consider two separate systems of fractional differential equations with exponential non-linearities. We also consider the corresponding systems of non-linear Volterra integral equations. We present results on the non-existence of global solutions for each system. Bounds on the blow-up time for each system are provided along with the asymptotic growth near blow-up. Each system can be regarded as a model for the interaction of two weakly diffusive media subjected to Arrhenius-type reactions. Our results indicate that a thermal blow-up cannot be avoided under such conditions.",

keywords = "anomalous diffusion, blow-up, fractional differential and integral equations, nonlinear Volterra equation",

author = "A. Kadem and M. Kirane and Kirk, {C. M.} and Olmstead, {W. E.}",

year = "2014",

month = aug,

day = "5",

doi = "10.1093/imamat/hxt005",

language = "English (US)",

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journal = "IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)",

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TY - JOUR

T1 - Blowing-up solutions to systems of fractional differential and integral equations with exponential non-linearities

AU - Kadem, A.

AU - Kirane, M.

AU - Kirk, C. M.

AU - Olmstead, W. E.

PY - 2014/8/5

Y1 - 2014/8/5

N2 - We consider two separate systems of fractional differential equations with exponential non-linearities. We also consider the corresponding systems of non-linear Volterra integral equations. We present results on the non-existence of global solutions for each system. Bounds on the blow-up time for each system are provided along with the asymptotic growth near blow-up. Each system can be regarded as a model for the interaction of two weakly diffusive media subjected to Arrhenius-type reactions. Our results indicate that a thermal blow-up cannot be avoided under such conditions.

AB - We consider two separate systems of fractional differential equations with exponential non-linearities. We also consider the corresponding systems of non-linear Volterra integral equations. We present results on the non-existence of global solutions for each system. Bounds on the blow-up time for each system are provided along with the asymptotic growth near blow-up. Each system can be regarded as a model for the interaction of two weakly diffusive media subjected to Arrhenius-type reactions. Our results indicate that a thermal blow-up cannot be avoided under such conditions.

KW - anomalous diffusion

KW - blow-up

KW - fractional differential and integral equations

KW - nonlinear Volterra equation

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VL - 79

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EP - 1088

JO - IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

JF - IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

IS - 6

ER -

Blowing-up solutions to systems of fractional differential and integral equations with exponential non-linearities

Abstract

Keywords

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