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| On a Strongly Damped Wave Equation for the Flame Front |
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Citation： |
Claude-Michel BRAUNER,Luca LORENZI,Gregory I. SIVASHINSKY,Chuanju XU.On a Strongly Damped Wave Equation for the Flame Front[J].Chinese Annals of Mathematics B,2010,31(6):819~840 |
| Page view： 2291
Net amount： 1195 |
Authors： |
Claude-Michel BRAUNER; Luca LORENZI; Gregory I. SIVASHINSKY; Chuanju XU; |
Foundation： |
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). |
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| Abstract： |
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 in-
volved. 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. |
Keywords： |
Front dynamics, Wave equation, Kuramoto-Sivashinsky equation,
Stability, Analytic semigroups, Spectral method |
Classification： |
35L05, 35B35, 35R35, 80A25 |
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