Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics

Ferruccio Colombini has been a Professor of Mathematical Analysis at the University of Pisa since 1986. His main interests are the theory of linear and nonlinear hyperbolic PDE's.Daniele Del Santo is Professor of Mathematical Analysis at the University of Trieste. He works in the field of hyperbolic and parabolic operators with non-smooth coefficients.David Lannes is CNRS Research Director at the Institut de Mathématiques de Bordeaux. He works on nonlinear PDEs and has a strong interest in applications to oceanography.

• 1 Amplitude equations for weakly nonlinear surface waves in variational problems.- 2 Global weak solutions of PDEs for compressible media: A compactness criterion to cover new physical situations.- 3 Second microlocalization and stabilization of damped wave equations on tori.- 4 A few remarks on hyperbolic systems with Zygmund in time coefficients.- 5 Well posedness of linearized Taylor equations in magnetohydrodynamics.- 6 Strictly dissipative non uniqueness with corners.- 7 On the solvability of certain degenerate partial differential operators.- 8 Location and Weyl formula for the eigenvalues of some non self-adjoint operators.- 9 A microscopic point of view on singularities in fluid models.- 10 Geometric optics for Rayleigh pulses in nonlinear elasticity.- 11 Recent results on stability of planar detonations.