This volume contains 14 research papers, which cover various topics, including blowup questions for quasilinear equations in 2-D, uniqueness results for systems of conservation laws in 1-D, conservation effects for critical nonlinear wave equations, diffraction of nonlinear waves, propagation of singularities in scattering theory,and caustics for semilinear oscillations. Other topics linked to microlocal analysis which are discussed are Sobolev spaces in Weyl-Hormander calculus, local solvability for pseudodifferential equations, and hypoellipticity for highly degenerate operators. A result for the Cauchy problem under partial analyticity assumptions and an article on the regularity of solutions for the characteristic initial boundary value problem are also included. Most of the papers contain detailed proofs which are accessible to graduate students and active researchers in connected areas.
Blowup of small data solutions for a class of quasilinear wave equations in two space dimensions - an outline of the proof, S. Alinhac; concentration effects in critical nonlinear wave equation and scattering theory, H. Bahouri and P. Gerard; lower semicontinuity of weighted path length in BV, P. Baiti and A. Bressan; time decay of Lp norms for solutions of the wave equation on exterior domains, M. Beals; Sobolev embeddings in Weyl-Hormander calculus, J-Y. Chemin and C-J. Xu; about the Cauchy problem for a system of conservation laws, C. Cheverry; global existance of the solutions and formation of singularities for a class of hyberbolic systems, D. DeL Santo, V. Georgiev and E. Mitidieri; a class of solvable operators, N. Dencker; uniqueness of the Cauchy problem under partial analyticity assumptions, L. Hormander; nonlinear wave diffraction, J.K. Hunter; caustics for dissipative semilinear oscillations, J-L. Joly, G. Metivier and J. Rauch; geometric optics and the bottom of the spectrum, R.B. Melrose; hypoellipticity for a class of infinately degenerate elliptic operators, Y. Morimoto and T. Morioka; regularity of solutions to characteristic boundary value problem for symmetric systems, T. Nishitani and M. Takayama.