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Nonlinear Evolution Equations That Change Type

  • Conference proceedings
  • © 1990

Overview

Editors:
  1. Barbara Lee Keyfitz

    1. Department of Mathematics, University of Houston, Houston, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Michael Shearer

    1. Department of Mathematics, North Carolina State University, Raleigh, USA

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: The IMA Volumes in Mathematics and its Applications (IMA, volume 27)

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Table of contents (19 papers)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Multiple Viscous Profile Riemann Solutions in Mixed Elliptic-Hyperbolic Models for Flow in Porous Media

    • A. V. Azevedo, D. Marchesin
    Pages 1-17

  3. On the Loss of Regularity of Shearing Flows of Viscoelastic Fluids

    • Bernard D. Coleman
    Pages 18-31

  4. Composite Type, Change of Type, and Degeneracy in First Order Systems with Applications to Viscoelastic Flows

    • L. Pamela Cook, G. Schleiniger, R. J. Weinacht
    Pages 32-46

  5. Numerical Simulation of Inertial Viscoelastic Flow with Change of Type

    • M. J. Crochet, V. Delvaux
    Pages 47-66

  6. Some Qualitative Properties of 2 × 2 Systems of Conservation Laws of Mixed Type

    • H. Holden, L. Holden, N. H. Risebro
    Pages 67-78

  7. On the Strict Hyperbolicity of the Buckley-Leverett Equations for Three-Phase Flow

    • Lars Holden
    Pages 79-84

  8. Admissibility Criteria and Admissible Weak Solutions of Riemann Problems for Conservation Laws of Mixed Type: A Summary

    • L. Hsiao
    Pages 85-88

  9. Shocks Near the Sonic Line: A Comparison between Steady and Unsteady Models for Change of Type

    • Barbara Lee Keyfitz
    Pages 89-106

  10. A Strictly Hyperbolic System of Conservation Laws Admitting Singular Shocks

    • Herbert C. Kranzer, Barbara Lee Keyfitz
    Pages 107-125

  11. An Existence and Uniqueness Result for Two Nonstrictly Hyperbolic Systems

    • Philippe Le Floch
    Pages 126-138

  12. Overcompressive Shock Waves

    • Tai-Ping Liu, Zhouping Xin
    Pages 139-145

  13. Quadratic Dynamical Systems Describing Shear Flow of Non-Newtonian Fluids

    • D. S. Malkus, J. A. Nohel, B. J. Plohr
    Pages 146-163

  14. Dynamic Phase Transitions: A Connection Matrix Approach

    • Konstantin Mischaikow
    Pages 164-180

  15. A Well-Posed Boundary Value Problem for Supercritical Flow of Viscoelastic Fluids of Maxwell Type

    • Michael Renardy
    Pages 181-191

  16. Loss of Hyperbolicity in Yield Vertex Plasticity Models under Nonproportional Loading

    • David G. Schaeffer, Michael Shearer
    Pages 192-217

  17. Undercompressive Shocks in Systems of Conservation Laws

    • Michael Shearer, Stephen Schecter
    Pages 218-231

  18. Measure Valued Solutions to a Backward-Forward Heat Equation: A Conference Report

    • M. Slemrod
    Pages 232-242

  19. One-Dimensional Thermomechanical Phase Transitions with Non-Convex Potentials of Ginzburg-Landau Type

    • Jürgen Sprekels
    Pages 243-257

  20. Admissibility of Solutions to the Riemann Problem for Systems of Mixed Type

    • Gerald Warnecke
    Pages 258-284
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Keywords

About this book

This IMA Volume in Mathematics and its Applications NONLINEAR EVOLUTION EQUATIONS THAT CHANGE TYPE is based on the proceedings of a workshop which was an integral part of the 1988-89 IMA program on NONLINEAR WAVES. The workshop focussed on prob­ lems of ill-posedness and change of type which arise in modeling flows in porous materials, viscoelastic fluids and solids and phase changes. We thank the Coordinat­ ing Committee: James Glimm, Daniel Joseph, Barbara Lee 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 workshop organizers, Barbara Lee Keyfitz and Michael Shearer, for their efforts in bringing together many of the major figures in those research fields in which theories for nonlinear evolution equations that change type are being developed. A vner Friedman Willard Miller, J r. ix PREFACE During the winter and spring quarters of the 1988/89 IMA Program on Non­ linear Waves, the issue of change of type in nonlinear partial differential equations appeared frequently. Discussion began with the January 1989 workshop on Two­ Phase Waves in Fluidized Beds, Sedimentation and Granular Flow; some of the papers in the proceedings of that workshop present strategies designed to avoid the appearance of change of type in models for multiphase fluid flow.

Editors and Affiliations

  • Department of Mathematics, University of Houston, Houston, USA

    Barbara Lee Keyfitz

  • Department of Mathematics, North Carolina State University, Raleigh, USA

    Michael Shearer

Bibliographic Information

  • Book Title: Nonlinear Evolution Equations That Change Type

  • Editors: Barbara Lee Keyfitz, Michael Shearer

  • Series Title: The IMA Volumes in Mathematics and its Applications

  • DOI: https://doi.org/10.1007/978-1-4613-9049-7

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1990

  • Hardcover ISBN: 978-0-387-97353-1Due: 24 September 1990

  • Softcover ISBN: 978-1-4613-9051-0Published: 14 October 2011

  • eBook ISBN: 978-1-4613-9049-7Published: 06 December 2012

  • Series ISSN: 0940-6573

  • Series E-ISSN: 2198-3224

  • Edition Number: 1

  • Number of Pages: XIV, 284

  • Topics: Partial Differential Equations, Physics, general

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