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The traveling waves for surface diffusion of plane curves are studied. Weconsider an evolving plane curve with two endpoints, which can move freely onthe x-axis with generating constant contact angles. For the evolution of thisplane curve governed by surface diffusion, we discuss the existence, theuniqueness and the convexity of traveling waves. The main results show that theuniqueness and the convexity can be lost in depending on the conditions of thecontact angles, although the existence holds for any contact angles in theinterval $(0,\pi/2)$.

Existence of non-convex traveling waves for surface diffusion of curves with constant contact angles