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Quarterly of Applied Mathematics
  
Online ISSN 1552-4485; Print ISSN 0033-569X
 

Decay of mass for fractional evolution equation with memory term


Authors: Ahmad Z. Fino, Hassan Ibrahim and Bilal Barakeh
Journal: Quart. Appl. Math. 71 (2013), 215-228
MSC (2010): Primary 35K55, 35B40
Published electronically: August 27, 2012
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Abstract: We investigate the decay properties of the mass $ M(t)= \int _{\mathbb{R}^N} u(\cdot ,t)dx$ of the solutions of a fractional diffusion equation with nonlinear memory term. We show, using a suitable class of initial data and a restriction on the diffusion and nonlinear term, that the memory term determines the large time asymptotics; that is, $ M(t)$ tends to zero as $ t\to \infty .$


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Additional Information

Ahmad Z. Fino
Affiliation: LaMA-Liban, Lebanese University, P.O. Box 37 Tripoli, Lebanon, and School of Arts and Sciences, Lebanese International University (LIU), Tripoli Campus, Dahr el Ain Road, Tripoli, Lebanon
Email: ahmad.fino01@gmail.com, afino@ul.edu.lb

Hassan Ibrahim
Affiliation: Lebanese University, Faculty of Sciences-I, Hadath, Beirut, Lebanon & LaMA-Liban, Lebanese University, P.O. Box 37 Tripoli, Lebanon, and School of Arts and Sciences, Lebanese International University (LIU), Beirut Campus, Al-Mouseitbeh, P.B. Box 14-6404, Beirut, Lebanon
Email: ibrahim@cermics.enpc.fr

Bilal Barakeh
Affiliation: LaMA-Liban, Lebanese University, P.O. Box 37 Tripoli, Lebanon
Email: bilal.barakeh@hotmail.com

DOI: http://dx.doi.org/10.1090/S0033-569X-2012-01286-4
PII: S 0033-569X(2012)01286-4
Keywords: Large time behavior of solutions, semilinear parabolic equation, fractional Laplacian
Received by editor(s): May 17, 2011
Published electronically: August 27, 2012
Article copyright: © Copyright 2012 Brown University



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