  By making use of the approximation method, we obtain the existence and
regularity of the viscosity solutions for the generalized mean curvature flow.
The asymptotic behavior of the flow is also considered. In particular, the
Dirichlet problem of the degenerate elliptic equation $$ -|\nabla
v|(\mathrm{div}(\frac{\nabla v}{|\nabla v|})+\nu)=0 $$ is solvable in viscosity
sense.
