Publications

2008

• Vector and scalar potentials, Poincaré's theorem and Korn's inequality
  
  • Amrouche Chérif
  • Ciarlet Philippe G.
  • Ciarlet Patrick
  , 2008. In this Note, we present several results concerning the vector potentials and the scalar potentials in a bounded, not necessarily simply-connected, three-dimensional domain. We consider also singular potentials corresponding to data in negative order Sobolev spaces. We also give some applications to Poincaré's theorem and to Korn's inequality.
• A new compactness result for electromagnetic waves. Application to the transmission problem between dielectrics and metamaterials
  
  • Bonnet-Ben Dhia Anne-Sophie
  • Ciarlet Patrick
  • Zwölf Carlo Maria
  Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2008, 18 (9), pp.1605-1631. We consider the time-harmonic Maxwell equations, involving wave transmission between media with opposite sign dielectric and/or magnetic coefficients. We prove that, in the case of sign-shifting dielectric coefficients, the space of electric fields is compactly embedded in L 2. We build a three-field variational formulation equivalent to Maxwell system for sign-shifting magnetic coefficients and show that, under some suitable conditions, the formulation fits into the coercive plus compact framework. © 2008 World Scientific Publishing Company. (10.1142/s0218202508003145)
  DOI : 10.1142/s0218202508003145
• The linear sampling method in a waveguide: A formulation based on modes
  
  • Bourgeois Laurent
  • Lunéville Éric
  Journal of Physics: Conference Series, IOP Science, 2008, 135 (-), pp.012023. This paper concerns the Linear Sampling Method to retrieve obstacles in a 2D or 3D acoustic waveguide. We derive a modal formulation of the LSM which is suitable for the waveguide configuration. Despite the ill-posedness of the inverse problem is increased owing to the evanescent modes, numerical experiments show good reconstruction of obstacles by using the far field. © 2008 IOP Publishing Ltd. (10.1088/1742-6596/135/1/012023)
  DOI : 10.1088/1742-6596/135/1/012023