Viscosity solutions of fully nonlinear parabolic systems

In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second-order degenerate parabolic equations and their Cauchy–Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perronʹs method with the technique of coupled solutions. The results here generalize those in Proc. London Math. Soc. 63 (1991) 212–240 and Comm. Partial Differential Equations 16 (1991) 1095–1128.