This book contains fourteen research papers which are expanded versions of conferences given at
a meeting held in September 1996 in Cortona Italy. The topics include blowup questions for
quasilinear equations in two dimensions time decay of waves in LP uniqueness results for
systems of conservation laws in one dimension concentra tion effects for critical nonlinear
wave equations diffraction of nonlin ear waves propagation of singularities in scattering
theory caustics for semi-linear oscillations. Other topics linked to microlocal analysis are
Sobolev embedding theorems in Weyl-Hormander calculus local solv ability for
pseudodifferential equations hypoellipticity for highly degen erate operators. The book also
contains a result on uniqueness for the Cauchy problem under partial analyticity assumptions
and an article on the regularity of solutions for characteristic initial-boundary value
problems. On each topic listed above one will find new results as well as a description of the
state of the art. Various methods related to nonlinear geometrical optics are a transversal
theme of several articles. Pseu dodifferential techniques are used to tackle classical PDE
problems like Cauchy uniqueness. We are pleased to thank the speakers for their contributions
to the meeting: Serge Alinhac Mike Beals Alberto Bressan Jean-Yves Chemin Christophe
Cheverry Daniele Del Santo Nils Dencker Patrick Gerard Lars Hormander John Hunter Richard
Melrose Guy Metivier Yoshinori Morimoto and Tatsuo Nishitani. The meeting was made possible
in part by the financial support of a European commission pro gram Human capital and mobility
CHRX-CT94-044.
