The parabolic quaternionic Monge-Ampère type equation on hyperKähler manifolds

We prove the long time existence and uniqueness of solution to a parabolic quaternionic Monge-Ampère type equation on a compact hyperKähler manifold. We also show that after normalization, the solution converges smoothly to the unique solution of the Monge-Ampère equation for $(n-1)$-quaternionic psh functions.