Publications

2016

• Study of a Model Equation in Detonation Theory: Multidimensional Effects
  
  • Faria Luiz
  • Kasimov A.
  • Rosales R.
  SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2016, 76 (3), pp.887-909. We extend the reactive Burgers equation presented in [A. R. Kasimov, L. M. Faria,and R. R. Rosales,Phys. Rev. Lett., 110 (2013), 104104], [L. M. Faria, A. R. Kasimov, and R. R.Rosales,SIAM J. Appl. Math., 74 (2014), pp. 547–570] to include multidimensional effects. Fur-thermore, we explain how the model can be rationally justified following the ideas of the asymptotictheory developed in [L. M. Faria, A. R. Kasimov, and R. R. Rosales,J. Fluid Mech., 784 (2015),pp. 163–198]. The proposed model is a forced version of the unsteady small disturbance transonicflow equations. We show that for physically reasonable choices of forcing functions, traveling wavesolutions akin to detonation waves exist. It is demonstrated that multidimensional effects play animportant role in the stability and dynamics of the traveling waves. Numerical simulations indicatethat solutions of the model tend to form multidimensional patterns analogous to cells in gaseousdetonations. (10.1137/15M1039663)
  DOI : 10.1137/15M1039663
• Mathematical Aspects of variational boundary integral equations for time dependent wave propagation
  
  • Joly Patrick
  • Rodríguez Jerónimo
  Journal of Integral Equations and Applications, Rocky Mountain Mathematics Consortium, 2016.
• Uniqueness results for inverse Robin problems with bounded coefficient
  
  • Baratchart Laurent
  • Bourgeois Laurent
  • Leblond Juliette
  Journal of Functional Analysis, Elsevier, 2016. In this paper we address the uniqueness issue in the classical Robin inverse problem on a Lipschitz domain $\Omega\subset\RR^n$, with $L^\infty$ Robin coefficient, $L^2$ Neumann data and isotropic conductivity of class $W^{1,r}(\Omega)$, $r>n$. We show that uniqueness of the Robin coefficient on a subpart of the boundary given Cauchy data on the complementary part, does hold in dimension $n=2$ but needs not hold in higher dimension. We also raise on open issue on harmonic gradients which is of interest in this context. (10.1016/j.jfa.2016.01.011)
  DOI : 10.1016/j.jfa.2016.01.011
• Iterative methods for scattering problems in isotropic or anisotropic elastic waveguides
  
  • Baronian Vahan
  • Bonnet-Ben Dhia Anne-Sophie
  • Fliss Sonia
  • Tonnoir Antoine
  Wave Motion, Elsevier, 2016. We consider the time-harmonic problem of the diffraction of an incident propagative mode by a localized defect, in an infinite straight isotropic elastic waveguide. We propose several iterative algorithms to compute an approximate solution of the problem, using a classical finite element discretization in a small area around the perturbation, and a modal expansion in unbounded straight parts of the guide. Each algorithm can be related to a so-called domain decomposition method, with or without an overlap between the domains. Specific transmission conditions are used, so that only the sparse finite element matrix has to be inverted, the modal expansion being obtained by a simple projection, using the Fraser bi-orthogonality relation. The benefit of using an overlap between the finite element domain and the modal domain is emphasized, in particular for the extension to the anisotropic case. The transparency of these new boundary conditions is checked for two- and three-dimensional anisotropic waveguides. Finally, in the isotropic case, numerical validation for two- and three-dimensional waveguides illustrates the efficiency of the new approach, compared to other existing methods, in terms of number of iterations and CPU time.
• A numerical study of the solution of x-mode equations around the hybrid resonance
  
  • Caldini-Queiros Céline
  • Després Bruno
  • Imbert-Gérard Lise-Marie
  • Kachanovska Maryna
  ESAIM: Proceedings and Surveys, EDP Sciences, 2016, 53, pp.1-21. Hybrid resonance is a physical phenomenon that appears for example in the heating of plasma, and as such is of scientific interest in the development of the ITER project. In this paper we focus some solutions with low regularity of Maxwell equations in plasmas under strong background magnetic field. Our purpose is two-fold. On one hand we investigate the finite element approximation of the one dimensional problem written in the frequency domain, and on the other hand we investigate two different finite difference approximations of the one dimensional time dependent problem. We will also compare the results of these different methods.