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arXiv · 2009.10016

Existence of global solutions and blow-up of solutions for coupled systems of fractional diffusion equations

A. Bashir·A. Alsaedi·M. Berbiche·M Kirane
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Abstract

We study the Cauchy problem for a system of semi-linear coupled fractional-diffusion equations with polynomial nonlinearities posed in $% \mathbb{R}_{+}\times \mathbb{R}^{N}$. 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.

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A. Bashir, A. Alsaedi, M. Berbiche, M Kirane. 2020-09-21. Existence of global solutions and blow-up of solutions for coupled systems of fractional diffusion equations. https://arxiv.org/abs/2009.10016

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