### Tuesday, May 20

10:00 AM-12:00 PM
*Maybird - Level C*

## MS29

Bifurcation Theory and Systems of Nonlinear Conservation Laws

Systems of two conservation laws in one space dimension are PDEs without viscosity that arise in modeling many physical systems, such as gas dynamics, three-phase flow in a porous medium, elastic strings, and phase transitions. The fundamental initial-value problem for these systems is the Riemann problem, in which the initial data are piecewise constant with a single jump. Riemann solutions can include shock waves, which are regarded as admissible if they correspond to traveling wave solutions when viscosity is added. This criterion may conflict with the classical Lax criterion. The speakers will discuss the use of vector field bifurcation theory to elucidate the wave structure of Riemann solutions.

**Organizer: Stephen Schecter**

*North Carolina State University *

**10:00 An Application of Vectorfield Bifurcation to Conservation Laws that Change Type**
- Barbara Lee Keyfitz, University of Houston
**10:30 On the Influence of Viscosity on Riemann Solutions of Nonlinear Conservation Laws**
- Suncica Canic, Iowa State University
**11:00 The Role of Polycycles in Nonuniqueness of Riemann Solutions**
- Arthur Azevedo, Universidade de Brasilia, Brazil; Dan Marchesin, Instituto de Matematica Pura e Aplicada, Brazil;
*Bradley Plohr*, State University of New York, Stony Brook; and Kevin Zumbrun, Indiana University
**11:30 Riemann Problem Solutions of Codimensions 0 and 1 **
*Stephen Schecter*, Organizer; Dan Marchesin, Instituto de Matematica Pura e Aplicada, Brazil; and Bradley Plohr, State University of New York, Stony Brook

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*TMP, 4/4/97*