The traveling waves for surface diffusion of plane curves are studied. We consider an evolving plane curve with two endpoints which can move freely on the x-axis with generating constant contact angles. For the evolution of this plane curve governed by surface diffusion, we discuss the existence, the uniqueness and the convexity of traveling waves. The main results show that the uniqueness and the convexity can be lost depending on the conditions of the contact angles, although the existence holds for any contact angles in the interval (0 , π/ 2).
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