Finite-time blowup for some nonlinear complex Ginzburg-Landau equations
In this article, we review finite-time blowup criteria for the family of complex Ginzburg-Landau equations $u_t = e^{ iθ} [Δu + |u|^αu] + γu$ on ${\mathbb R}^N $, where $0 \le θ\le \frac {π} {2}$, $α>0$ and $γ\in {\mathbb R} $. We study in particular the effect of the parameters $θ$ and $γ$, and the dependence of the blowup time on these parameters.
math.AP↗