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.
Uniqueness of entropy solutions for doubly nonlinear anisotropic degenerate parabolic equations by M. Bendahmane and K. H. Karlsen Nonlinear regularizations of TV based PDEs for image processing by A. Bertozzi, J. Greer, S. Osher, and K. Vixie Wave generation by a moving boundary by J. L. Bona and V. V. Varlamov Analysis on models for exothermically reacting, compressible flows with large discontinuous initial data by G.-Q. Chen and K. Trivisa Eulerian-Lagrangian hydrodynamic equations by P. Constantin Quantum hydrodynamic models derived from the entropy principle by P. Degond, F. Mehats, and C. Ringhofer Mathematics of viscous, compressible, and heat conducting fluids by E. Feireisl Symmetry-breaking bifurcations for free boundary problems by A. Friedman Errors in numerical solutions of spherically symmetric shock physics problems by J. Glimm, J. W. Grove, Y. Kang, T. Lee, X. Li, D. H. Sharp, K. Q. Ye, Y. Yu, and M. Zhao Existence to solutions of a kinetic aerosol model by P.-E. Jabin and C. Klingenberg Functional analytic methods for evolution systems by J. W. Jerome Stability of Riemann solutions with large oscillation for the Euler equations by Y. Li Some recent results on instability of ideal plane flows by Z. Lin Boundary conditions for an ocean related system with a small parameter by A. Rousseau, R. Temam, and J. Tribbia A remark on Y. Brenier's approach to Born-Infeld electro-magnetic fields by D. Serre On recent developments in the spectral problem for the linearized Euler equation by R. Shvydkoy and S. Friedlander Transonic flow arising from 2-D Riemann problems by K. Song A note on long-time behavior of solutions to the Boussinesq system at large Prandtl number by X. Wang.