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 language | British English |
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Pages (from-to) | 103-135 |
Number of pages | 33 |
Journal | Taiwanese Journal of Mathematics |
Volume | 26 |
Issue number | 1 |
DOIs | |
State | Published - Feb 2022 |
Keywords
- blow-up
- coupled fractional-wave equations
- global solution
- polynomial nonlinearities