Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

  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
Published electronically: September 9, 2011
MathSciNet review: 2920620
Full-text PDF

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC (2000): 26A33, 35B33, 35K55, 74G25, 74H35, 74G40

Retrieve articles in all journals with MSC (2000): 26A33, 35B33, 35K55, 74G25, 74H35, 74G40

Additional Information

Ahmad Z. Fino
Affiliation: LaMA-Liban, Lebanese University, P.O. Box 37 Tripoli, Lebanon

Mokhtar Kirane
Affiliation: Département de Mathématiques, Pôle Sciences et Technologies, Université de la Rochelle, Avenue M. Crépeau, La Rochelle 17042, France

PII: S 0033-569X(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

Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2015 Brown University
AMS Website