TY - JOUR
T1 - On a strongly damped wave equation for the flame front
AU - Brauner, Claude Michel
AU - Lorenzi, Luca
AU - Sivashinsky, Gregory I.
AU - Xu, Chuanju
N1 - Funding Information:
Manuscript received June 24, 2010. Published online October 22, 2010. ∗School of Mathematical Sciences, Xiamen University, 361005 Xiamen, Fujian, China. ∗∗Dipartimento di Matematica, Università degli Studi di Parma, Viale Parco Area delle Scienze 53/A, 43124 Parma, Italy. ∗∗∗School of Mathematical Sciences, Tel Aviv University, 69978 Tel Aviv, Israel. ∗∗∗∗Corresponding author. School of Mathematical Sciences, Xiamen University, 361005 Xiamen, Fujian, China. E-mail: cjxu@xmu.edu.cn ∗∗∗∗∗Project supported by the National Natural Science Foundation of China (No. 11071203), the 973 High Performance Scientific Computation Research Program (No. 2005CB321703), the US-Israel Binational Science Foundation (No. 2006-151) and the Israel Science Foundation (No. 32/09).
PY - 2010/11
Y1 - 2010/11
N2 - 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.
AB - 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.
KW - Analytic semigroups
KW - Front dynamics
KW - Kuramoto-Sivashinsky equation
KW - Spectral method
KW - Stability
KW - Wave equation
UR - http://www.scopus.com/inward/record.url?scp=78650202430&partnerID=8YFLogxK
U2 - 10.1007/s11401-010-0616-1
DO - 10.1007/s11401-010-0616-1
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AN - SCOPUS:78650202430
SN - 0252-9599
VL - 31
SP - 819
EP - 840
JO - Chinese Annals of Mathematics. Series B
JF - Chinese Annals of Mathematics. Series B
IS - 6
ER -