Viscosity solutions of fully nonlinear parabolic systems. (Q1399325)

The authors prove the existence, uniqueness and continuity of viscosity solutions of the Cauchy-Dirichlet problem for weakly coupled, nonlinear, second order, degenerate parabolic equations. The proof uses the Perron method in combination with the technique of coupled sub and super viscosity solutions. The results are a generalization of previous work of \textit{H. Engler} and \textit{S. M. Lenhart} [Proc. Lond. Math. Soc. (3) 63, 212--240 (1991; Zbl 0704.35030)] for systems of first order Hamilton-Jacobi equations, and of \textit{H. Ishii} and \textit{S. Koike} [Commun. Partial Differ. Equations 16, 1095--1128 (1991; Zbl 0742.35022)] for monotone systems of fully nonlinear second order elliptic equations.