Fast Reactions and the Stefan Free Boundary Problem

  • Benoît Perthame
Chapter
Part of the Lecture Notes on Mathematical Modelling in the Life Sciences book series (LMML)

Abstract

We continue in the direction of asymptotic analysis. Departing from reaction-diffusion systems, we consider the fast reaction limit in two specific example of systems. We show how the Stefan free boundary problem arises in this fast reaction limit. Depending on the unscaled reaction-diffusion system, two cases are recovered, with or without latent heat. Because of the strong nonlinearity, compactness is needed to justify the asymptotic behavior. This relies on estimates in the space of functions with bounded variation. Various numerical simulations illustrate the complex dynamics generated by the Stefan free boundary problem.

Keywords

Asymptotic analysis Fast reaction limit Latent heat Stefan free boundary problem 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Benoît Perthame
    • 1
  1. 1.Université Pierre et Marie CurieParisFrance

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