Convergence of the Weak Kahler-Ricci Flow on Manifolds of General Type

We study the Kahler-Ricci flow on compact Kahler manifolds whose canonical bundle is big. We show that the normalized Kahler-Ricci flow has long-time existence in the viscosity sense, is continuous in a Zariski open set, and converges to the unique singular Kahler-Einstein metric in the canonical class. The key ingredient is a viscosity theory for degenerate complex Monge-Ampere flows in big classes that we develop, extending and refining the approach of Eyssidieux-Guedj-Zeriahi.