For the Lorentz manifold M^2xR, with M^2 a 2-dimensional complete surface with nonnegative Gaussian curvature, we investigate its space-like graphs over compact strictly convex domains in M^2, which are evolving by the non-parametric mean curvature flow with prescribed contact angle boundary condition, and show that solutions converge to ones moving only by translation. This talk is based on a joint-work with L. Chen, D.-D. Hu and N. Xiang.

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