Nonlinear Partial Differential Equations
About this Title
Gui-Qiang Chen and Emmanuele DiBenedetto, Editors
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 cross-section 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.
Graduate students and research mathematicians interested in nonlinear partial differential equations and related topics; physicists, engineers, and computational scientists.
Table of Contents
- Paolo Baiti, Philippe G. LeFloch and Benedetto Piccoli – Nonclassical shocks and the Cauchy problem: general conservation laws [MR 1724652]
- Luis A. Caffarelli – The Harnack inequality and non-divergence equations [MR 1724653]
- Gui-Qiang Chen and Hermano Frid – Vanishing viscosity limit for initial-boundary value problems for conservation laws [MR 1724654]
- Alexandre J. Chorin, Anton P. Kast and Raz Kupferman – On the prediction of large-scale dynamics using unresolved computations [MR 1724655]
- Peter Constantin – Variational bounds in turbulent convection [MR 1724656]
- Bernard Dacorogna and Paolo Marcellini – On the solvability of implicit nonlinear systems in the vectorial case [MR 1724657]
- Constantine M. Dafermos – Genuinely nonlinear hyperbolic systems of two conservation laws [MR 1724658]
- Irene M. Gamba – Milne problem for strong force scaling [MR 1724659]
- James Glimm, John W. Grove, X. L. Li and N. Zhao – Simple front tracking [MR 1724660]
- Yan Guo and A. Shadi Tahvildar-Zadeh – Formation of singularities in relativistic fluid dynamics and in spherically symmetric plasma dynamics [MR 1724661]
- Corrado Lattanzio and Pierangelo Marcati – Asymptotic stability of plane diffusion waves for the $2$-D quasilinear wave equation [MR 1724662]
- Tai-Ping Liu and Tong Yang – $L_1$ stability for systems of hyperbolic conservation laws [MR 1724663]
- Tian Ma and Shouhong Wang – The geometry of the stream lines of steady states of the Navier-Stokes equations [MR 1724664]
- Rolando Magnanini and Giorgio Talenti – On complex-valued solutions to a $2$-D eikonal equation. I. Qualitative properties [MR 1724665]
- Uwe F. Mayer and Gieri Simonett – On diffusion-induced grain-boundary motion [MR 1724666]
- Mike O’Leary – Local estimates for solutions to singular and degenerate quasilinear parabolic equations [MR 1724667]
- Danping Peng, Stanley Osher, Barry Merriman and Hong-Kai Zhao – The geometry of Wulff crystal shapes and its relations with Riemann problems [MR 1724668]