Nonlinear Elliptic Problems with Critical Exponent in Shrinking Annuli.
Nonlinear evolution PDEs in : existence and uniqueness of solutions, asymptotic and Borel summability properties
Nonlinear Pulse Propagation
This talk gives a brief review of some recent progress in the asymptotic analysis of short pulse solutions of nonlinear hyperbolic partial differential equations. This includes descriptions on the scales of geometric optics and diffractive geometric optics, and also studies of special situations where pulses passing through focal points can be analysed.
Numerical study of acoustic multiperforated plates
It is rather classical to model multiperforated plates by approximate impedance boundary conditions. In this article we would like to compare an instance of such boundary conditions obtained through a matched asymptotic expansions technique to direct numerical computations based on a boundary element formulation in the case of linear acoustic.