Multidimensional Hyperbolic Problems and Computations

1. Front Matter

   Pages i-xiv

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2. Macroscopic Limits of Kinetic Equations

   • Claude Bardos, François Golse, David Levermore

   Pages 1-12

3. The Essence of Particle Simulation of the Boltzmann Equation

   • H. Babovsky, R. Illner

   Pages 13-22

4. The Approximation of Weak Solutions to the 2-D Euler Equations by Vortex Elements

   • J. Thomas Beale

   Pages 23-37

5. Limit Behavior of Approximate Solutions to Conservation Laws

   • Chen Gui-Qiang

   Pages 38-57

6. Modeling Two-Phase Flow of Reactive Granular Materials

   • Pedro F. Embid, Melvin R. Baer

   Pages 58-67

7. Shocks Associated with Rotational Modes

   • Heinrich Freistühler

   Pages 68-69

8. Self-Similar Shock Reflection in Two Space Dimensions

   • Harland M. Glaz

   Pages 70-88

9. Nonlinear Waves: Overview and Problems

   • James Glimm

   Pages 89-106

10. The Growth and Interaction of Bubbles in Rayleigh-Taylor Unstable Interfaces

    • James Glimm, Xiao Lin Li, Ralph Menikoff, David H. Sharp, Qiang Zhang

    Pages 107-122

11. Front Tracking, Oil Reservoirs, Engineering Scale Problems and Mass Conservation

    • James Glimm, Brent Lindquist, Qiang Zhang

    Pages 123-139

12. Collisionless Solutions to the Four Velocity Broadwell Equations

    • J. M. Greenberg, Cleve Moler

    Pages 140-155

13. Anomalous Reflection of a Shock Wave at a Fluid Interface

    • John W. Grove, Ralph Menikoff

    Pages 156-168

14. An Application of Connection Matrix to Magnetohydrodynamic Shock Profiles

    • Harumi Hattori, Konstantin Mischaikow

    Pages 169-172

15. Convection of Discontinuities in Solutions of the Navier-Stokes Equations for Compressible Flow

    • David Hoff

    Pages 173-178

16. Nonlinear Geometrical Optics

    • John K. Hunter

    Pages 179-197

17. Geometric Theory of Shock Waves

    • Tai-Ping Liu

    Pages 198-202

18. An Introduction to front Tracking

    • Christian Klingenberg, Bradley Plohr

    Pages 203-216

19. One Perspective on Open Problems in Multi-Dimensional Conservation Laws

    • Andrew J. Majda

    Pages 217-238

20. Stability of Multi-Dimensional Weak Shocks

    • Guy Métivier

    Pages 239-250

This IMA Volume in Mathematics and its Applications MULTIDIMENSIONAL HYPERBOLIC PROBLEMS AND COMPUTATIONS is based on the proceedings of a workshop which was an integral part ofthe 1988-89 IMA program on NONLINEAR WAVES. We are grateful to the Scientific Commit­ tee: James Glimm, Daniel Joseph, Barbara Keyfitz, Andrew Majda, Alan Newell, Peter Olver, David Sattinger and David Schaeffer for planning and implementing an exciting and stimulating year-long program. We especially thank the Work­ shop Organizers, Andrew Majda and James Glimm, for bringing together many of the major figures in a variety of research fields connected with multidimensional hyperbolic problems. A vner Friedman Willard Miller PREFACE A primary goal of the IMA workshop on Multidimensional Hyperbolic Problems and Computations from April 3-14, 1989 was to emphasize the interdisciplinary nature of contemporary research in this field involving the combination of ideas from the theory of nonlinear partial differential equations, asymptotic methods, numerical computation, and experiments. The twenty-six papers in this volume span a wide cross-section of this research including some papers on the kinetic theory of gases and vortex sheets for incompressible flow in addition to many papers on systems of hyperbolic conservation laws. This volume includes several papers on asymptotic methods such as nonlinear geometric optics, a number of articles applying numerical algorithms such as higher order Godunov methods and front­ tracking to physical problems along with comparison to experimental data, and also several interesting papers on the rigorous mathematical theory of shock waves.

• differential equation
• hyperbolic system
• partial differential equation
• singularity
• stability

• Department of Applied Mathematics and Statistics, SUNY at Stony Brook, Stony Brook, USA

  James Glimm

• Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, Princeton, USA

  Andrew J. Majda

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