Open Access
February, 2022 Global Existence and Blow-up of Solutions for a System of Fractional Wave Equations
Bashir Ahmad, Ahmed Alsaedi, Mohamed Berbiche, Mokhtar Kirane
Author Affiliations +
Taiwanese J. Math. 26(1): 103-135 (February, 2022). DOI: 10.11650/tjm/210804


We investigate the Cauchy problem for a $2 \times 2$-system of weakly coupled semi-linear fractional wave equations with polynomial nonlinearities posed in $\mathbb{R}^{+} \times \mathbb{R}^{N}$. Under appropriate conditions on the exponents and the fractional orders of the time derivatives, it is shown that there exists a threshold value of the dimension $N$, for which, small data-global solutions as well as finite time blowing-up solutions exist. Furthermore, we investigate the $L^{\infty}$-decay estimates of global solutions.

Funding Statement

This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, Saudi Arabia under grant no. (KEP-PHD-80-130-42). The authors, therefore, acknowledge with thanks DSR technical and financial support.


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Bashir Ahmad. Ahmed Alsaedi. Mohamed Berbiche. Mokhtar Kirane. "Global Existence and Blow-up of Solutions for a System of Fractional Wave Equations." Taiwanese J. Math. 26 (1) 103 - 135, February, 2022.


Received: 25 May 2020; Revised: 26 April 2021; Accepted: 30 August 2021; Published: February, 2022
First available in Project Euclid: 8 September 2021

MathSciNet: MR4367788
zbMATH: 1494.35044
Digital Object Identifier: 10.11650/tjm/210804

Primary: 26A33 , 35J05 , 35L15

Keywords: Blow-up , coupled fractional-wave equations , global solution , polynomial nonlinearities

Rights: Copyright © 2022 The Mathematical Society of the Republic of China

Vol.26 • No. 1 • February, 2022
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