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Nonlinear Partial Differential Equations and Related Analysis
Edited by: Gui-Qiang Chen, George Gasper, and Joseph Jerome, Northwestern University, Evanston, IL
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Contemporary Mathematics
2005; 321 pp; softcover
Volume: 371
ISBN-10: 0-8218-3533-5
ISBN-13: 978-0-8218-3533-3
List Price: US$98
Member Price: US$78.40
Order Code: CONM/371
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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.

Readership

Graduate students and research mathematicians interested in partial differential equations.

Table of Contents

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