Traveling waves for the closed hypersurfaces in central force fields

We consider the front propagation problems for the hyperbolic mean curvature motion in central force fields. Problems of this type describe the long time behavior for the electrically charged membrane with a constant charge per area and a radially symmetric potential moving with the mean curvature motion law. In this paper, we establish the existence of generalized periodic traveling waves with a large speed of propagation under appropriate assumptions on the central periodic force fields.