Traveling Waves and Shocks in a Viscoelastic Generalization of Burgers' Equation

We consider traveling wave phenomena for a viscoelastic generalization of Burgers' equation. For asymptotically constant velocity profiles we find three classes of solutions corresponding to smooth traveling waves, piecewise smooth waves, and piecewise constant (shock) solutions. Each solution type is possible for a given pair of asymptotic limits and we characterize the dynamics in terms of the relaxation time and viscosity. Key words. non-Newtonian fluids, fast-slow dynamics, vanishing viscosity solutions AMS subject classifications. 35L67, 76A10, 35Q53

• Type: Journal
• Year: 2008
• Where: SIAMAM
• Authors: Victor Camacho, Robert D. Guy, Jon Jacobsen
• Keywords: SIAMAM 2008, Solutions, Viscoelastic Generalization, Waves