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.
© 2008 Society for Industrial and Applied Mathematics
V. Camacho, R. Guy, and J. Jacobsen. "Traveling Waves and Shocks in a Viscoelastic Generalization of Burgers Equation," SIAM J. Appl. Math., (2008) Vol. 68, pp. 1316-1332.
This article is also available from the Society for Industrial and Applied Mathematics at http://dx.doi.org/10.1137/070687840.