Qualitative properties of solutions to a time-space fractional evolution equation

Ahmad Z. Fino; Mokhtar Kirane

doi:10.1090/S0033-569X-2011-01246-9

Qualitative properties of solutions to a time-space fractional evolution equation

Ahmad Z. Fino, Mokhtar Kirane

Mathematics

Lebanese University

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

62 Scopus citations

Abstract

In this article, we analyze a spatio-temporally nonlocal nonlinear parabolic equation. First, we validate the equation by an existence-uniqueness result. Then, we show that blowing-up solutions exist and study their time blow-up profile. Also, a result on the existence of global solutions is presented. Furthermore, we establish necessary conditions for local or global existence.

Original language	British English
Pages (from-to)	133-157
Number of pages	25
Journal	Quarterly of Applied Mathematics
Volume	70
Issue number	1
DOIs	https://doi.org/10.1090/S0033-569X-2011-01246-9
State	Published - 2012

Keywords

Blow-up rate
Critical exponent
Fractional Laplacian
Local existence
Parabolic equation
Riemann-Liouville fractional integrals and derivatives

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10.1090/S0033-569X-2011-01246-9

Cite this

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AB - In this article, we analyze a spatio-temporally nonlocal nonlinear parabolic equation. First, we validate the equation by an existence-uniqueness result. Then, we show that blowing-up solutions exist and study their time blow-up profile. Also, a result on the existence of global solutions is presented. Furthermore, we establish necessary conditions for local or global existence.

KW - Blow-up rate

KW - Critical exponent

KW - Fractional Laplacian

KW - Local existence

KW - Parabolic equation

KW - Riemann-Liouville fractional integrals and derivatives

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Qualitative properties of solutions to a time-space fractional evolution equation

Abstract

Keywords

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