David Ketcheson, KAUST

KAUST-IAMCS Workshop on Multiscale Modeling, Advanced Discretization Techniques, and Simulation of Wave Propagation

May 7-8, 2011

King Abdullah University of Science and Technology (KAUST)

Thuwal, Kingdom of Saudi Arabia

Shock Dynamics in Layered Periodic Media

Solutions of constant-coefficient nonlinear hyperbolic PDEs generically develop shocks, even if the initial data is smooth. Solutions of hyperbolic PDEs with variable coefficients can behave very differently. We investigate formation and stability of shock waves in a one-dimensional periodic layered medium. By studying time-reversibility and entropy evolution, we find that weak shocks are unstable in such media. Furthermore, the formation of shocks in such media can be predicted based on a characteristic condition that is a generalization of the classical Lax entropy condition.