Critical exponents of Fujita type for certain evolution equations and systems with spatio-temporal fractional derivatives

M. Kirane; Y. Laskri; N. E. Tatar

doi:10.1016/j.jmaa.2005.03.054

Critical exponents of Fujita type for certain evolution equations and systems with spatio-temporal fractional derivatives

M. Kirane, Y. Laskri, N. E. Tatar

Mathematics

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

110 Scopus citations

Abstract

This paper is concerned with establishing necessary or sufficient conditions for the existence of solutions to evolution equations with fractional derivatives in space and time. The Fujita exponent is determined. Then, these results are extended to systems of reaction-diffusion equations. Our new results shed lights on important practical questions.

Original language	British English
Pages (from-to)	488-501
Number of pages	14
Journal	Journal of Mathematical Analysis and Applications
Volume	312
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2005.03.054
State	Published - 15 Dec 2005

Keywords

Fractional derivatives
Fujita's exponent
Nonlinear evolution equations
Nonlinear reaction-diffusion systems
Porous media

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10.1016/j.jmaa.2005.03.054

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title = "Critical exponents of Fujita type for certain evolution equations and systems with spatio-temporal fractional derivatives",

abstract = "This paper is concerned with establishing necessary or sufficient conditions for the existence of solutions to evolution equations with fractional derivatives in space and time. The Fujita exponent is determined. Then, these results are extended to systems of reaction-diffusion equations. Our new results shed lights on important practical questions.",

keywords = "Fractional derivatives, Fujita's exponent, Nonlinear evolution equations, Nonlinear reaction-diffusion systems, Porous media",

author = "M. Kirane and Y. Laskri and Tatar, {N. E.}",

note = "Funding Information: The third author expresses his gratitude to King Fahd University of Petroleum and Minerals for its financial support.",

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AU - Kirane, M.

AU - Laskri, Y.

AU - Tatar, N. E.

N1 - Funding Information: The third author expresses his gratitude to King Fahd University of Petroleum and Minerals for its financial support.

PY - 2005/12/15

Y1 - 2005/12/15

N2 - This paper is concerned with establishing necessary or sufficient conditions for the existence of solutions to evolution equations with fractional derivatives in space and time. The Fujita exponent is determined. Then, these results are extended to systems of reaction-diffusion equations. Our new results shed lights on important practical questions.

AB - This paper is concerned with establishing necessary or sufficient conditions for the existence of solutions to evolution equations with fractional derivatives in space and time. The Fujita exponent is determined. Then, these results are extended to systems of reaction-diffusion equations. Our new results shed lights on important practical questions.

KW - Fractional derivatives

KW - Fujita's exponent

KW - Nonlinear evolution equations

KW - Nonlinear reaction-diffusion systems

KW - Porous media

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ER -

Critical exponents of Fujita type for certain evolution equations and systems with spatio-temporal fractional derivatives

Abstract

Keywords

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