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arXiv · 2010.03309

Global existence and blow-up of solutions for a system of fractional wave equations

Ahmad Bashir·Mohamed Berbiche·Ahmed Elsaedi·Mokhtar Kirane
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Abstract

We investigate the Cauchy problem for a 2x2-system of weakly coupled semi-linear fractional wave equations with polynomial nonlinearities posed in R+ x RN. 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 L1-decay estimates of global solutions.

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Ahmad Bashir, Mohamed Berbiche, Ahmed Elsaedi, Mokhtar Kirane. 2020-10-07. Global existence and blow-up of solutions for a system of fractional wave equations. https://arxiv.org/abs/2010.03309

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