Nonlinear Partial Differential Equations and Related Analysis
About this Title
Gui-Qiang Chen, George Gasper and Joseph Jerome, Editors
The Emphasis Year on Nonlinear Partial Differential Equations and Related Analysis at Northwestern University produced this fine collection of original research and survey articles. Many well-known mathematicians attended the events and submitted their contributions for this volume.
Eighteen papers comprise this work, representing the most significant advances and current trends in nonlinear PDEs and their applications. Topics covered include elliptic and parabolic equations, Navier Stokes equations, and hyperbolic conservation laws. Important applications are presented from incompressible and compressible fluid mechanics, combustion, and electromagnetism. Also included are articles on recent advances in statistical reliability in modeling, simulation, level set methods for image processing, shock waves, free boundaries, boundary layers, errors in numerical solutions, stability, instability, and singular limits.
The volume is suitable for researchers and graduate students interested in partial differential equations.
Graduate students and research mathematicians interested in partial differential equations.
Table of Contents
- Mostafa Bendahmane and Kenneth H. Karlsen – Uniqueness of entropy solutions for doubly nonlinear anisotropic degenerate parabolic equations [MR 2143857]
- Andrea Bertozzi, John Greer, Stanley Osher and Kevin Vixie – Nonlinear regularizations of TV based PDEs for image processing [MR 2143858]
- Jerry L. Bona and Vladimir V. Varlamov – Wave generation by a moving boundary [MR 2143859]
- Gui-Qiang Chen and Konstantina Trivisa – Analysis on models for exothermically reacting, compressible flows with large discontinous initial data [MR 2143860]
- Peter Constantin – Eulerian-Lagrangian hydrodynamic equations [MR 2143861]
- Pierre Degond, Florian Méhats and Christian Ringhofer – Quantum hydrodynamic models derived from the entropy principle [MR 2143862]
- Eduard Feireisl – Mathematics of viscous, compressible, and heat conducting fluids [MR 2143863]
- Avner Friedman – Symmetry-breaking bifurcations for free boundary problems [MR 2143864]
- James Glimm, John W. Grove, Yunghee Kang, Taewon Lee, Xiaolin Li, David H. Sharp, Kenny Q. Ye, Yan Yu and Ming Zhao – Errors in numerical solutions of spherically symmetric shock physics problems [MR 2143865]
- Pierre-Emmanuel Jabin and Christian Klingenberg – Existence to solutions of a kinetic aerosol model [MR 2143866]
- Joseph W. Jerome – Functional analytic methods for evolution systems [MR 2143867]
- Yachun Li – Stability of Riemann solutions with large oscillation for the Euler equations [MR 2143868]
- Zhiwu Lin – Some recent results on instability of ideal plane flows [MR 2143869]
- A. Rousseau, R. Temam and J. Tribbia – Boundary conditions for an ocean related system with a small parameter [MR 2143870]
- Denis Serre – A remark on Y. Brenier’s approach to Born-Infeld electro-magnetic fields [MR 2143871]
- Roman Shvydkoy and Susan Friedlander – On recent developments in the spectral problem for the linearized Euler equation [MR 2143872]
- Kyungwoo Song – Transonic flow arising from 2-D Riemann problems [MR 2143873]
- Xiaoming Wang – A note on long time behavior of solutions to the Boussinesq system at large Prandtl number [MR 2143874]