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

Cyrill Muratov, M. Novaga

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)521-547
Number of pages27
JournalCalculus of Variations and Partial Differential Equations
Volume31
Issue number4
DOIs
StatePublished - Apr 1 2008

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Front Propagation
Singular Limit
Minimizer
Advection
Advection-diffusion-reaction Equation
Converge
Existence-uniqueness
Variational Approach
Free Boundary Problem
Traveling Wave Solutions
Free Boundary
Variational Problem
Combustion
Monotonicity
Upper and Lower Bounds
Curvature
Decay
Numerical Examples
Modeling

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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Front propagation in infinite cylinders. II. the sharp reaction zone limit. / Muratov, Cyrill; Novaga, M.

In: Calculus of Variations and Partial Differential Equations, Vol. 31, No. 4, 01.04.2008, p. 521-547.

Research output: Contribution to journalArticle

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