The aim of this book is to present hyperbolic partial di?erential equations at an elementary level. In fact, the required mathematical background is only a third year university course on di?erential calculus for functions of several variables. No functional analysis knowledge is needed, nor any distribution theory (with the exception of shock waves mentioned below). k All solutions appearing in the text are piecewise classical C solutions. Beyond the simpli?cations it allows, there are several reasons for this choice: First, we believe that all main features of hyperbolic partial d-...

Presents two essential and apparently unrelated subjects that include, microlocal analysis and the theory of pseudo-differential operators, a basic tool in the study of partial differential equations and in analysis on manifolds; and the Nash-Moser theorem

The content of this book corresponds to a one-semester course taught at the University of Paris-Sud (Orsay) in the spring 1994. It is accessible to students or researchers with a basic elementary knowledge of Partial Dif ferential Equations, especially of hyperbolic PDE (Cauchy problem, wave operator, energy inequality, finite speed of propagation, symmetric systems, etc.). This course is not some final encyclopedic reference gathering all avail able results. We tried instead to provide a short synthetic view of what we believe are the main results obtained so far, with self-contained proofs....