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2008, Volume 1, Issue 1: 27-39. Doi: 10.3934/dcdss.2008.1.27
This issue Previous Article Counting uniformly attracting solutions of nonautonomous differential equations Next Article Incompressible fluids with shear rate and pressure dependent viscosity: Regularity of steady planar flows

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

  • 2.

    Department of Mathematical Sciences, Indiana University – Purdue University Indianapolis, Indianapolis, IN 46202-3216

  • 3.

    Faculty of Sciences – Mathematics and Computer Science division, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081HV Amsterdam

  • 4.

    Dipartimento di Matematica, Università di Parma, Viale G. Usberti 85/A, 43100 Parma

  • 5.

    School of Mathematical Sciences, Tel Aviv University

Received:  August 31, 2006
Revised:  September 30, 2007
Published:  February 2008
Abstract Related Papers Cited by
    Abstract
  • 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.

    Citation:
    shu

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