A Kaehler-Ricci flow on functions

Question

Let $(M,\omega)$ be a Kaehler manifold. The Ricci form is noted $\rho (\omega)$. A Kaehler-Ricci flow on functions is defined by the formula:

$$\frac{\partial \phi}{\partial t}=  \star   \partial \bar \partial  \star \rho(\omega+\partial \bar \partial \phi)$$

with $\star$ the Hodge operator on exterior forms.

Can we find solutions of the Kaehler-Ricci flow on functions? Does it converge?