  Blow-up phenomena ofvweakly coupled systems of several evolution equations,
especially complex Ginzburg-Landau equationsvis shown by a straightforward ODE
approach not so-called test-function method, which gives the natural blow-up
rate. The difficulty of the proof is that, unlike the single case, terms which
come from the fact that the Laplacian cannot be absorbed into the weakly
coupled nonlinearities. A similar ODE approach is applied to heat systems by
Mochizuki to obtain the lower estimate of lifespan.
