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

Fino, Ahmad; Kirane, Mokhtar

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

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: 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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