On a strongly damped wave equation for the flame front

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 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.

Keywords

Front dynamics / Wave equation / Kuramoto-Sivashinsky equation / Stability / Analytic semigroups / Spectral method

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