Calculus of Variations and Geometric Measure Theory
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C. Muratov - M. Novaga

Front propagation in infinite cylinders II. The sharp reaction zone limit

created by novaga on 10 Nov 2018

[BibTeX]

Published Paper

Inserted: 10 nov 2018
Last Updated: 10 nov 2018

Journal: Calc. Var. PDE
Volume: 31
Pages: 521-547
Year: 2008

Abstract:

This paper applies the variational approach developed in part I of this work 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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