Contemporary Mathematics 1999; 303 pp; softcover Volume: 238 ISBN10: 0821811967 ISBN13: 9780821811962 List Price: US$73 Member Price: US$58.40 Order Code: CONM/238
 This volume is a collection of original research papers and expository articles stemming from the scientific program of the Nonlinear PDE Emphasis Year held at Northwestern University (Evanston, IL) in March 1998. The book offers a crosssection of the most significant recent advances and current trends and directions in nonlinear partial differential equations and related topics. The book's contributions offer two perspectives. There are papers on general analytical treatment of the theory and papers on computational methods and applications originating from significant realistic mathematical models of natural phenomena. Also included are articles that bridge the gap between these two perspectives, seeking synergistic links between theory and modeling and computation. The volume offers direct insight into recent trends in PDEs. Readership Graduate students and research mathematicians interested in nonlinear partial differential equations and related topics; physicists, engineers, and computational scientists. Table of Contents  P. Baiti, P. G. LeFloch, and B. Piccoli  Nonclassical shocks and the Cauchy problem: General conservation laws
 L. A. Caffarelli  The Harnack inequality and nondivergence equations
 G.Q. Chen and H. Frid  Vanishing viscosity limit for initialboundary value problems for conservation laws
 A. J. Chorin, A. P. Kast, and R. Kupferman  On the prediction of largescale dynamics using unresolved computations
 P. Constantin  Variational bounds in turbulent convection
 B. Dacorogna and P. Marcellini  On the solvability of implicit nonlinear systems in the vectorial case
 C. M. Dafermos  Genuinely nonlinear hyperbolic systems of two conservation laws
 I. M. Gamba  Milne problem for strong force scaling
 J. Glimm, J. W. Grove, X. L. Li, and N. Zhao  Simple front tracking
 Y. Guo and A. S. TahvildarZadeh  Formation of singularities in relativistic fluid dynamics and in spherically symmetric plasma dynamics
 C. Lattanzio and P. Marcati  Asymptotic stability of plane diffusion waves for the \(2\)\(D\) quasilinear wave equation
 T.P. Liu and T. Yang  \(L_1\) stability for systems of hyperbolic conservation laws
 T. Ma and S. Wang  The geometry of the stream lines of steady states of the NavierStokes equations
 R. Magnanini and G. Talenti  On complexvalued solutions to a 2D eikonal equation. Part one: Qualitative properties
 U. F. Mayer and G. Simonett  On diffusioninduced grainboundary motion
 M. O'Leary  Local estimates for solutions to singular and degenerate quasilinear parabolic equations
 D. Peng, S. Osher, B. Merriman, and H.K. Zhao  The geometry of Wulff crystal shapes and its relations with Riemann problems
