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Advances in Pure and Applied Mathematics

Editor-in-Chief: Trimeche, Khalifa

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Online
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1869-6090
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Steady state solutions to the conserved Kuramoto–Sivashinsky equation

Hela Trojette
  • LAMFA, CNRS UMR 6140, Université de Picardie Jules Verne, UFR Science, 33, rue Saint-Leu 80039 Amiens, France
  • :
/ Ayman Eldoussouki
  • LAMFA, CNRS UMR 6140, Université de Picardie Jules Verne, UFR Science, 33, rue Saint-Leu 80039 Amiens, France
  • :
/ Mohamed Abaidi
  • LAMFA, CNRS UMR 6140, Université de Picardie Jules Verne, UFR Science, 33, rue Saint-Leu 80039 Amiens, France
  • :
/ Mohammed Guedda
  • LAMFA, CNRS UMR 6140, Université de Picardie Jules Verne, UFR Science, 33, rue Saint-Leu 80039 Amiens, France
  • :
Published Online: 2012-01-19 | DOI: https://doi.org/10.1515/apam.2011.010

Abstract.

We study stationary solutions to the conserved Kuramoto–Sivashinsky equation th+y2f48(f+12)h+y2h+f12(yh)2=0. This equation has recently been proposed to describe the step meandering instability on a vicinal surface. Attention is focussed on stationary periodic solutions which are the key for the coarsening process.

Keywords.: Conserved Kuramoto–Sivashinsky equation; crystal growth; stationary periodic solution


Received: 2011-04-10

Accepted: 2011-05-14

Published Online: 2012-01-19

Published in Print: 2012-01-01


Citation Information: Advances in Pure and Applied Mathematics. Volume 3, Issue 1, Pages 59–65, ISSN (Online) 1869-6090, ISSN (Print) 1867-1152, DOI: https://doi.org/10.1515/apam.2011.010, January 2012

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