Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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

Authors: Ahmad Z. Fino and Mokhtar Kirane
Journal: Quart. Appl. Math. 70 (2012), 133-157
MSC (2000): Primary 26A33, 35B33, 35K55; Secondary 74G25, 74H35, 74G40
DOI: https://doi.org/10.1090/S0033-569X-2011-01246-9
Published electronically: September 9, 2011
MathSciNet review: 2920620
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Abstract | References | Similar Articles | Additional Information

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.

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Additional Information

Ahmad Z. Fino
Affiliation: LaMA-Liban, Lebanese University, P.O. Box 37 Tripoli, Lebanon
Email: ahmad.fino01@gmail.com

Mokhtar Kirane
Affiliation: Département de Mathématiques, Pôle Sciences et Technologies, Université de la Rochelle, Avenue M. Crépeau, La Rochelle 17042, France
Email: mokhtar.kirane@univ-lr.fr

DOI: https://doi.org/10.1090/S0033-569X-2011-01246-9
Keywords: Parabolic equation, fractional Laplacian, Riemann-Liouville fractional integrals and derivatives, local existence, critical exponent, blow-up rate
Received by editor(s): August 10, 2010
Published electronically: September 9, 2011
Article copyright: © Copyright 2011 Brown University

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