Coarsening in an interfacial equation without slope selection revisited: Analytical results

In this Letter, we re-examen a one-dimensional model of epitaxial growth that describes pyramidal structures characterized by the absence of a preferred slope [L. Golubović, Phys. Rev. Lett. 78 (1997) 90]. A similarity approach shows that the typical mound lateral size and the interfacial width growth with time like t1/2 and t1/4, respectively. This result was previously presented by Golubović. Our contribution provides a mathematical justification for the existence of similarity solutions which correspond to, or predict, the typical coarsening process.