Global Existence and Blow-up of Solutions for a System of Fractional Wave Equations

Bashir Ahmad, Ahmed Alsaedi, Mohamed Berbiche, Mokhtar Kirane

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

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

Original languageBritish English
Pages (from-to)103-135
Number of pages33
JournalTaiwanese Journal of Mathematics
Volume26
Issue number1
DOIs
StatePublished - Feb 2022

Keywords

  • blow-up
  • coupled fractional-wave equations
  • global solution
  • polynomial nonlinearities

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