Non-existence of global solutions to a system of fractional diffusion equations

M. Kirane; B. Ahmad; A. Alsaedi; M. Al-Yami

doi:10.1007/s10440-014-9865-4

Non-existence of global solutions to a system of fractional diffusion equations

M. Kirane, B. Ahmad, A. Alsaedi, M. Al-Yami

Mathematics

King Abdulaziz University

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

34 Scopus citations

Abstract

We present non-existence results for a system of non-linear parabolic equations with non-local diffusions posed either in ℝ^N or in a bounded domain. Our method of proof is based on the test function method with a judicious choice of the test function.

Original language	British English
Pages (from-to)	235-248
Number of pages	14
Journal	Acta Applicandae Mathematicae
Volume	133
Issue number	1
DOIs	https://doi.org/10.1007/s10440-014-9865-4
State	Published - Oct 2014

Keywords

Blow-up solutions
Fractional calculus
Nonlocal operators
Systems of reaction-diffusion equations

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abstract = "We present non-existence results for a system of non-linear parabolic equations with non-local diffusions posed either in ℝN or in a bounded domain. Our method of proof is based on the test function method with a judicious choice of the test function.",

keywords = "Blow-up solutions, Fractional calculus, Nonlocal operators, Systems of reaction-diffusion equations",

author = "M. Kirane and B. Ahmad and A. Alsaedi and M. Al-Yami",

note = "Funding Information: Acknowledgement This paper was funded by the King Abdulaziz University under Grant No. (15/34/Gr). The authors, therefore, acknowledge the technical and financial support of KAU.",

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AU - Ahmad, B.

AU - Alsaedi, A.

AU - Al-Yami, M.

N1 - Funding Information: Acknowledgement This paper was funded by the King Abdulaziz University under Grant No. (15/34/Gr). The authors, therefore, acknowledge the technical and financial support of KAU.

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KW - Blow-up solutions

KW - Fractional calculus

KW - Nonlocal operators

KW - Systems of reaction-diffusion equations

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Non-existence of global solutions to a system of fractional diffusion equations

Abstract

Keywords

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