Thursday, August 10
MS15
Conservation Laws: Traveling Waves and Other Self-Similar Solutions - Part I of II
10:00 AM-12:00 PM
Orchard & Pikake (Salon 7 & 8)
For Part II, see MS20.
Hyperbolic conservation laws, systems of nonlinear PDEs of the form U_t+F(U)_x=0, and related equations with source terms, have self-similar solutions with discontinuities (shock waves). When diffusion terms are included, the shock waves become smooth traveling waves, which correspond to heteroclinic solutions of ODEs. Existence of traveling waves is studied using bifurcation theory, geometric singular perturbation theory, or topological methods. Stability can
be studied using the Evans function thanks to recent developments. The speakers will explore new ideas in this
area, and applications including phase transitions, combustion, porous media flow, and thin films.
Organizers: Stephen Schecter and Michael Shearer
North Carolina State University, USA
- 10:00-10:25 Undercompressive Shocks in Driven Film Flow
- Andrea Bertozzi, Duke University, USA; A. Munch, Technische Universität München, Germany; and Michael Shearer, Organizer
- 10:30-10:55 Pointwise Estimates and Nonlinear Stability for Viscous Shock Waves
- Peter Howard, Courant Institute of Mathematical Sciences, New York University, USA; and Kevin Zumbrun, Indiana University, USA
- 11:00-11:25 Instability of Viscous Shock Waves in Generalized p-Systems
- Jian Deng and Christopher K. R. T. Jones, Brown University, USA
- Cancelled
11:30-11:55 Stability of Combustion Waves
Kevin Zumbrun, Indiana University, USA
- 11:30-11:55 Travelling Waves in Thin Film Flow
- Michael Shearer, Organizer