TY - JOUR
AU - Coclite, Giuseppe Maria
AU - Di Ruvo, Lorenzo
PY - 2022/09/30
Y2 - 2024/08/04
TI - On the Classical Solutions for the Kuramoto-Sivashinsky Equation with Ehrilch-Schwoebel Effects
JF - Contemporary Mathematics
JA - Contemp. Math.
VL - 3
IS - 4
SE - Research Article
DO - 10.37256/cm.3420221607
UR - https://ojs.wiserpub.com/index.php/CM/article/view/1607
SP - 386-431
AB - <p>The Kuramoto-Sivashinsky equation with Ehrilch-Schwoebel effects models the evolution of surface morphology during Molecular Beam Epitaxy growth, provoked by an interplay between deposition of atoms onto the surface and the relaxation of the surface profile through surface diffusion. It consists of a nonlinear fourth order partial differential equation. Using energy methods we prove the well-posedness (i.e., existence, uniqueness and stability with respect to the initial data) of the classical solutions for the Cauchy problem, associated with this equation.</p>
ER -