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

Authors

  • Giuseppe Maria Coclite Department of Mechanics, Mathematics and Management, Polytechnic University of Bari, via E. Orabona 4, 70125 Bari, Italy https://orcid.org/0000-0001-6019-4757
  • Lorenzo Di Ruvo Department of Mathematics, University of Bari, via E. Orabona 4, 70125 Bari, Italy

DOI:

https://doi.org/10.37256/cm.3420221607

Keywords:

existence, uniqueness, stability, the Kuramoto-Sivashinsky equation with Ehrilch-Schwoebel effects, Cauchy problem

Abstract

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.

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Published

2022-09-30

How to Cite

1.
Coclite GM, Di Ruvo L. On the Classical Solutions for the Kuramoto-Sivashinsky Equation with Ehrilch-Schwoebel Effects. Contemp. Math. [Internet]. 2022 Sep. 30 [cited 2024 Jul. 18];3(4):386-431. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/1607