Instabilities in certain one-dimensional singular interfacial equation

Abstract

We re-examine a generalized singular equation to discuss the coarsening of growing interfaces, in the presence of Ehrlich-Schwoebel-Villain barrier that induces a pyramidal or mound-type structure without slope selection. Our aim is to obtain analytically results on the coarsening process by inspecting the behavior of branch of the steady state periodic solutions.

On the Classical Solutions for the Kuramoto-Sivashinsky Equation with Ehrilch-Schwoebel Effects

“…For that reason, it is known as the Ehrilch-Schwoebel (ES) barrier (see also [3,4]). The ES barrier induces pyramidal or mound-type structures on the growing surface (see also [5][6][7][8][9][10][11][12]). In particular, in [5], the authors study the following equation: (1 ( ) )…”

“…, which is present in Equation (7). In [5], the authors study the coarsening process that may result from Equation (7), with n > 0, n ≠ 1, called n− model. In particular, the authors give an analytical justification of solutions to n− model, which correspond to, or predict, the coarsening process.…”