Weak solutions to degenerate complex Monge-Amp\'ere flows I

Studying the (long-term) behavior of the K"ahler-Ricci flow on mildly singular varieties, one is naturally lead to study weak solutions of degenerate parabolic complex Monge-Amp'ere equations. The purpose of this article, the first of a series on this subject, is to develop a viscosity theory for degenerate complex Monge-Amp`ere flows in domains of ${\text{C}}^n$.