Publications

2002

• Homogenization and localization for a 1-D eigenvalue problem in a periodic medium with an interface
  
  • Allaire Grégoire
  • Capdeboscq Yves
  Annali di Matematica Pura ed Applicata, Springer Verlag, 2002, 181 (3), pp.247--282. In one space dimension we address the homogenization of the spectral problem for a singularly perturbed diffusion equation in a periodic medium. Denoting by the period, the diffusion coefficient is scaled as 2. The domain is made of two purely periodic media separated by an interface. Depending on the connection between the two cell spectral equations, three different situations arise when goes to zero. First, there is a global homogenized problem as in the case without an interface. Second, the limit is made of two homogenized problems with a Dirichlet boundary condition on the interface. Third, there is an exponential localization near the interface of the first eigenfunction. (10.1007/s102310100040)
  DOI : 10.1007/s102310100040
• MULTIFLUID IONIZATION MODELS
  
  • Buet Christophe
  • Cordier Stéphane
  • Raviart Pierre-Arnaud
  Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2002, 12, pp.17-48. In this paper, we present a multi-fluid ionization model. We prove that this stationary, mono-dimensional model has a maximal solution which is not global at variance with the mono-species case and we present a numerical method for solving this highly singular system of ordinary differential equations. Numerical results are compared with those obtained for other models.