Annali dell’Università di Ferrara

, Volume 46, Issue 1, pp 175–180 | Cite as

A note on the nonexistence of monotonic steady solutions of the Kuramoto-Sivashinsky equation

  • Naoyuki Ishimura
  • Masaaki Nakamura


We present a simple proof of the nonexistence of monotonic solutions derived from the Kuramoto-Sivashinsky equation. Although our method restricts the range of parameters, it has the advantage of applicability to other equations, which includes a model of dendritic growth of needle crystals.


Travel Wave Solution Dendritic Growth Heteroclinic Orbit Steady Solution Laminar Flame 
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In questo lavoro, presentiamo una semplice dimostrazione di non esistenza di soluzioni monotone per l’equazione di Kuramoto-Sivashinsky. Sebbene il nostro metodo restringa il range dei parametri, esso ha il vantaggio di essere applicabile anche ad equazioni aventi interesse fisico quali descriventi un modello locale di solidificazione.


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Copyright information

© Università degli Studi di Ferrara 2000

Authors and Affiliations

  • Naoyuki Ishimura
    • 1
  • Masaaki Nakamura
    • 2
  1. 1.Department of MathematicsHitotsubashi UniversityTokyoJapan
  2. 2.College of Science and TechnologyNihon UniversityTokyoJapan

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