  We study the parabolic complex Monge-Amp\`ere type equations on closed
Hermitian manfolds. We derive uniform $C^\infty$ {\em a priori} estimates for
normalized solutions, and then prove the $C^\infty$ convergence. The result
also yields a way to carry out method of continuity for elliptic Monge-Amp\'ere
type equations.

Analysis of PDEs;Differential Geometry