TY - JOUR
T1 - Dissipativity for a semi-linearized system modeling cellular flames
AU - Frankel, Michael
AU - Roytburd, Victor
AU - Sivashinsky, Gregory
PY - 2011/2
Y1 - 2011/2
N2 - 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.
AB - 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.
KW - Attractors
KW - Dissipative systems
KW - Hausdorff dimension
KW - Kuramoto-Sivashinsky equation
UR - http://www.scopus.com/inward/record.url?scp=84864462223&partnerID=8YFLogxK
U2 - 10.3934/dcdss.2011.4.83
DO - 10.3934/dcdss.2011.4.83
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AN - SCOPUS:84864462223
VL - 4
SP - 83
EP - 99
JO - Discrete and Continuous Dynamical Systems - Series S
JF - Discrete and Continuous Dynamical Systems - Series S
SN - 1937-1632
IS - 1
ER -