BRAUNER, Claude-Michel; LORENZI, Luca; SIVASHINSKY, Gregory I.; XU, Chuanju

doi:10.1007/s11401-010-0616-1

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BRAUNER, Claude-Michel
Institut de Mathématiques de Bordeaux [IMB]
Xiamen University

LORENZI, Luca
Dipartimento di Matematica

SIVASHINSKY, Gregory I.
School of Mathematical Sciences

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Chinese Annals of Mathematics - Series B. 2010-11, vol. 31, n° 6, p. 22

Springer Verlag

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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.< Leer menos

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Front dynamics

Wave equation

Kuramoto-Sivashinsky equation

Stability

Analytic semigroups

Spectral method

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On a strongly damped wave equation for the flame front

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