Dissipativity for a semi-linearized system modeling cellular flames

Michael Frankel, Victor Roytburd, Gregory Sivashinsky

Research output: Contribution to journalArticlepeer-review


We study a Semi-Linearized System (SLS) of second order PDEs modeling flame front dynamics. SLS is a simplified version of the weak κθ model of cellular flames which is dynamically similar to the Kuramoto-Sivashinsky (KS) equation [7, 4]. We prove existence of the solutions at large, and their proximity, for finite time, to the solutions of KS. We demonstrate that SLS possesses a universal absorbing set and a compact attractor. Furthermore, we show that the attractor is of finite Hausdorff dimension.

Original languageEnglish
Pages (from-to)83-99
Number of pages17
JournalDiscrete and Continuous Dynamical Systems - Series S
Issue number1
StatePublished - Feb 2011


  • Attractors
  • Dissipative systems
  • Hausdorff dimension
  • Kuramoto-Sivashinsky equation


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