Dynamical properties of a nonlinear Kuramoto-Sivashinsky growth equation

Mohammed Benlahsen (1) , Gabriella Bognar , Zoltan Csati (2) , Mohammed Guedda (3) , Krisztian Hriczo

1 LPMC - Laboratoire de Physique de la Matière Condensée - UR UPJV 2081
2 LaMcube - Laboratoire de Mécanique, Multiphysique, Multiéchelle - UMR 9013
3 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

The conserved Kuramoto-Sivashinsky equation can be considered as the one- and twodimensional evolution equation for amorphous thin film growth. The role of the nonlinear term Dojruj2THORN and the properties of the solutions are investigated analytically and numerically. Analytical results of wavelength and amplitude are provided. Numerical simulations of this equation are presented, showing the roughening and coarsening of the surface pattern and the evolution of the surface morphology over time for different parameter values in one- and two-dimensions. (C)2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

Domaines: Mathématiques [math]

Mohammed Benlahsen, Gabriella Bognar, Zoltan Csati, Mohammed Guedda, Krisztian Hriczo. Dynamical properties of a nonlinear Kuramoto-Sivashinsky growth equation. Alexandria Engineering Journal, 2021, 60 (3), pp.3419-3427. ⟨10.1016/j.aej.2021.02.003⟩. ⟨hal-03621254⟩