Front propagation in infinite cylinders. II. The sharp reaction zone limit |
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Authors: | C B Muratov M Novaga |
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Institution: | (1) Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA;(2) Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, Pisa, 56127, Italy |
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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. |
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Keywords: | 35R35 35J60 35J20 |
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