TY - JOUR
T1 - A fully nonlinear equation for the flame front in a quasi-steady combustion model
AU - Brauner, Claude Michel
AU - Hulshof, Josephus
AU - Lorenzi, Luca
AU - Sivashinsky, Gregory I.
PY - 2010/8
Y1 - 2010/8
N2 - We revisit the Near Equidiffusional Flames (NEF) model introduced by Matkowsky and Sivashinsky in 1979 and consider a simplified, quasisteady version of it. This simplification allows, near the planar front, an explicit derivation of the front equation. The latter is a pseudodifferential fully nonlinear parabolic equation of the fourth-order. First, we study the (orbital) stability of the null solution. Second, introducing a parameter ε, we rescale both the dependent and independent variables and prove rigourously the convergence to the solution of the Kuramoto-Sivashinsky equation as ε → 0.
AB - We revisit the Near Equidiffusional Flames (NEF) model introduced by Matkowsky and Sivashinsky in 1979 and consider a simplified, quasisteady version of it. This simplification allows, near the planar front, an explicit derivation of the front equation. The latter is a pseudodifferential fully nonlinear parabolic equation of the fourth-order. First, we study the (orbital) stability of the null solution. Second, introducing a parameter ε, we rescale both the dependent and independent variables and prove rigourously the convergence to the solution of the Kuramoto-Sivashinsky equation as ε → 0.
KW - Front dynamics
KW - Fully nonlinear equations
KW - Kuramoto-Sivashinsky equation
KW - Pseudo-differential operators
KW - Stability
UR - http://www.scopus.com/inward/record.url?scp=77954328124&partnerID=8YFLogxK
U2 - 10.3934/dcds.2010.27.1415
DO - 10.3934/dcds.2010.27.1415
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AN - SCOPUS:77954328124
SN - 1078-0947
VL - 27
SP - 1415
EP - 1446
JO - Discrete and Continuous Dynamical Systems
JF - Discrete and Continuous Dynamical Systems
IS - 4
ER -