On a strongly damped wave equation for the flame front

Claude-Michel Brauner (1, 2) , Luca Lorenzi (3) , Gregory I. Sivashinsky (4) , Chuanju Xu (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 Xiamen University
3 Dipartimento di Matematica
4 School of Mathematical Sciences

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.

Mots clés: Front dynamics; Wave equation; Kuramoto-Sivashinsky equation; Stability; Analytic semigroups; Spectral method

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Science non linéaire [physics]

Claude-Michel Brauner, Luca Lorenzi, Gregory I. Sivashinsky, Chuanju Xu. On a strongly damped wave equation for the flame front. Chinese Annals of Mathematics - Series B, 2010, 31 (6), pp.22. ⟨10.1007/s11401-010-0616-1⟩. ⟨hal-01261852⟩