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

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  • 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.
    Mathematics Subject Classification: Primary: 35K55, 35B25; Secondary: 80A25.


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