Proceedings of Symposia in Applied Mathematics 2007; 217 pp; hardcover Volume: 65 ISBN10: 0821842110 ISBN13: 9780821842119 List Price: US$50 Member Price: US$40 Order Code: PSAPM/65
 The articles of this book are written by leading experts in partial differential equations and their applications, who present overviews here of recent advances in this broad area of mathematics. The formation of shocks in fluids, modern numerical computation of turbulence, the breaking of the Einstein equations in a vacuum, the dynamics of defects in crystals, effects due to entropy in hyperbolic conservation laws, the NavierStokes and other limits of the Boltzmann equation, occupancy times for Brownian motion in a two dimensional wedge, and new methods of analyzing and solving integrable systems are some of this volume's subjects. The reader will find an exposition of important advances without a lot of technicalities and with an emphasis on the basic ideas of this field. Readership Graduate students and research mathematicians interested in partial differential equations. Table of Contents  S. Klainerman  Null hypersurfaces with finite curvature flux and a breakdown criterion in general relativity
 D. Christodoulou  The formation of shocks in 3dimensional fluids
 F. A. Grünbaum and C. McGrouther  Occupation time for two dimensional Brownian motion in a wedge
 R. Buckingham, A. Tovbis, S. Venakides, and X. Zhou  The semiclassical focusing nonlinear Schrödinger equation
 Y. Li  An extension to a classical theorem of Liouville and applications
 A. S. Fokas  From Green to Lax via Fourier
 J. Jimenéz  Untangling wall turbulence through direct simulations
 L. L. Bonilla and A. Carpio  Defects, singularities and waves
 C. D. Levermore  Fluid dynamics from Boltzmann equations
 F. Golse  From the Boltzmann equation to the incompressible NavierStokes equations
 C. M. Dafermos  Hyperbolic conservation laws with involutions and contingent entropies
