Remarks on large time behavior of level-set mean curvature flow equations with driving and source terms

We study a level-set mean curvature flow equation with driving and source terms, and establish convergence results on the asymptotic behavior of solutions as time goes to infinity under some additional assumptions. We also study the associated stationary problem in details in a particular case, and establish Alexandrov's theorem in two dimensions in the viscosity sense, which is of independent interest.