Traveling curved fronts of anisotropic curvature flows

Abstract

In this paper, the anisotropic curvature flows with driving force are considered. The existence of traveling curved fronts is shown by constructing supersolutions and subsolutions. By the advantage of this method, their global stability is also proved. In the last section the profiles of the traveling fronts are discussed when the anisotropy becomes strong and converges to a non-smooth function.