Decay of mass for fractional evolution equation with memory term

Fino, Ahmad; Ibrahim, Hassan; Barakeh, Bilal

doi:10.1090/S0033-569X-2012-01286-4

Authors: Ahmad Z. Fino, Hassan Ibrahim and Bilal Barakeh
Journal: Quart. Appl. Math. 71 (2013), 215-228
MSC (2010): Primary 35K55, 35B40
DOI: https://doi.org/10.1090/S0033-569X-2012-01286-4
Published electronically: August 27, 2012
MathSciNet review: 3087420
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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, tends to zero as $t\to \infty .$

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