Weakly coupled systems of fully nonlinear parabolic equations in the Heisenberg group

This paper is devoted to viscosity solutions to weakly coupled systems of fully nonlinear parabolic equations in the first Heisenberg group. We extend well-posedness results in the Euclidean space to the Heisenberg group, including the uniqueness and existence of solutions with exponential growth at space infinity under monotonicity and other regularity assumptions on the parabolic operators. In addition, Lipschitz preserving properties of the system are also studied. (C) 2018 Elsevier Ltd. All rights reserved.