TY - JOUR

T1 - Front propagation in infinite cylinders. II. the sharp reaction zone limit

AU - Muratov, C. B.

AU - Novaga, M.

PY - 2008/4

Y1 - 2008/4

N2 - This paper applies the variational approach developed in part I of this work [22] to a singular limit of reaction-diffusion-advection equations which arise in combustion modeling. We first establish existence, uniqueness, monotonicity, asymptotic decay, and the associated free boundary problem for special traveling wave solutions which are minimizers of the considered variational problem in the singular limit. We then show that the speed of the minimizers of the approximating problems converges to the speed of the minimizer of the singular limit. Also, after an appropriate translation the minimizers of the approximating problems converge strongly on compacts to the minimizer of the singular limit. In addition, we obtain matching upper and lower bounds for the speed of the minimizers in the singular limit in terms of a certain area-type functional for small curvatures of the free boundary. The conclusions of the analysis are illustrated by a number of numerical examples.

AB - This paper applies the variational approach developed in part I of this work [22] to a singular limit of reaction-diffusion-advection equations which arise in combustion modeling. We first establish existence, uniqueness, monotonicity, asymptotic decay, and the associated free boundary problem for special traveling wave solutions which are minimizers of the considered variational problem in the singular limit. We then show that the speed of the minimizers of the approximating problems converges to the speed of the minimizer of the singular limit. Also, after an appropriate translation the minimizers of the approximating problems converge strongly on compacts to the minimizer of the singular limit. In addition, we obtain matching upper and lower bounds for the speed of the minimizers in the singular limit in terms of a certain area-type functional for small curvatures of the free boundary. The conclusions of the analysis are illustrated by a number of numerical examples.

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U2 - 10.1007/s00526-007-0125-6

DO - 10.1007/s00526-007-0125-6

M3 - Article

AN - SCOPUS:38849197508

SN - 0944-2669

VL - 31

SP - 521

EP - 547

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 4

ER -