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.
|Number of pages||17|
|Journal||Discrete and Continuous Dynamical Systems - Series S|
|State||Published - Feb 2011|
- Dissipative systems
- Hausdorff dimension
- Kuramoto-Sivashinsky equation