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.

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