Bashir Ahmad, Ahmed Alsaedi, Mohamed Berbiche, Mokhtar Kirane
Abstract:
We study the Cauchy problem for a system of semi-linear coupled
fractional-diffusion equations with polynomial nonlinearities posed in
. Under appropriate conditions on the
exponents and the orders of the fractional time derivatives, we present a
critical value of the dimension N, for which global solutions with small
data exist, otherwise solutions blow-up in finite time. Furthermore, the
large time behavior of global solutions is discussed.
Submitted May 1, 2019. Published November 2, 2020.
Math Subject Classifications: 35A01, 35R09, 35K10, 45K05.
Key Words: Coupled fractional-diffusion equations; polynomial nonlinearities;
global solution; blow-up.
DOI: 10.58997/ejde.2020.110
Show me the PDF file (425 KB), TEX file for this article.
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Bashir Ahmad NAAM Research Group, Department of Mathematics Faculty of Science King Abdulaziz University, P.O. Box 80203 Jeddah 21589, Saudi Arabia email: bashirahmad_qau@yahoo.com |
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Ahmed Alsaedi NAAM Research Group, Department of Mathematics Faculty of Science King Abdulaziz University, P.O. Box 80203 Jeddah 21589, Saudi Arabia email: aalsaedi@hotmail.com |
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Mohamed Berbiche Laboratory of Mathematical Analysis, Probability and Optimizations Mohamed Khider University, Biskra, PO. Box 145 Biskra (07000) Algeria email: berbichemed@yahoo.fr, mohamed.berbiche@univ-biskra.dz |
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Mokhtar Kirane Department of Mathematics and Statistics College of Art and Sciences Khalifa University of Science and Technology Abu Dhabi, United Arab Emirates email: mokhtar.kirane@ku.ac.ae, mokhtar.kirane@univ-lr.fr |
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