The parabolic Monge-Amp\`ere equation on compact almost Hermitian manifolds

We prove the long time existence and uniqueness of solutions to the parabolic Monge-Amp`ere equation on compact almost Hermitian manifolds. We also show that the normalization of solution converges to a smooth function in $C^{\mathrm{\infty }}$ topology as $t\to \mathrm{\infty }$. Up to scaling, the limit function is a solution of the Monge-Amp`ere equation. This gives a parabolic proof of existence of solutions to the Monge-Amp`ere equation on almost Hermitian manifolds.