# American Institute of Mathematical Sciences

March  2008, 1(1): 27-39. doi: 10.3934/dcdss.2008.1.27

## On the κ - θ model of cellular flames: Existence in the large and asymptotics

 1 Institut de Mathématiques de Bordeaux, Université Bordeaux 1, 33405 Talence cedex, France 2 Department of Mathematical Sciences, Indiana University – Purdue University Indianapolis, Indianapolis, IN 46202-3216, United States 3 Faculty of Sciences – Mathematics and Computer Science division, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081HV Amsterdam, Netherlands 4 Dipartimento di Matematica, Università di Parma, Viale G. Usberti 85/A, 43100 Parma, Italy 5 School of Mathematical Sciences, Tel Aviv University

Received  September 2006 Revised  October 2007 Published  December 2007

We consider the κ - θ model of flamefront dynamics introduced in [6]. We show that a space-periodic problem for the lattersystem of two equations is globally well-posed. We prove that nearthe instability threshold the front is arbitrarily close to thesolution of the Kuramoto-Sivashinsky equation on a fixed timeinterval if the evolution starts from close configurations.The dynamics generated by the model isillustrated by direct numerical simulation.
Citation: Claude-Michel Brauner, Michael L. Frankel, Josephus Hulshof, Alessandra Lunardi, G. Sivashinsky. On the κ - θ model of cellular flames: Existence in the large and asymptotics. Discrete & Continuous Dynamical Systems - S, 2008, 1 (1) : 27-39. doi: 10.3934/dcdss.2008.1.27
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