Asymptotic behavior of Type III mean curvature flow on noncompact   hypersurfaces
  In this paper, we introduce a monotonicity formula for the mean curvature flow which is related to self-expanders. Then we use the monotonicity to study the asymptotic behavior of Type III mean curvature flow on noncompact hypersurfaces. 
Liang Cheng, Natasa Sesum
math.DG