Generalized complex Monge-Ampere equation

Question

Let $(M,\omega)$ be a Kaehler manifold, we can generalize the Ricci flow by adding the Laplacian of the symplectic forms. We obtain the generalized complex Monge-Ampere flow:

$$\frac{\partial \phi}{\partial t}+\lambda \Delta (\phi)=log(\omega_0+\partial \bar{\partial} \phi)^n$$

Can we find solutions of the generalized complex Monge-Ampere equation?