On a strongly damped wave equation for the flame front

Claude Michel Brauner, Luca Lorenzi, Gregory I. Sivashinsky, Chuanju Xu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In two-dimensional free-interface problems, the front dynamics can be modeled by single parabolic equations such as the Kuramoto-Sivashinsky equation (K-S). However, away from the stability threshold, the structure of the front equation may be more involved. In this paper, a generalized K-S equation, a nonlinear wave equation with a strong damping operator, is considered. As a consequence, the associated semigroup turns out to be analytic. Asymptotic convergence to K-S is shown, while numerical results illustrate the dynamics.

Original languageEnglish
Pages (from-to)819-840
Number of pages22
JournalChinese Annals of Mathematics. Series B
Issue number6
StatePublished - Nov 2010


  • Analytic semigroups
  • Front dynamics
  • Kuramoto-Sivashinsky equation
  • Spectral method
  • Stability
  • Wave equation


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