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

Authors

Victor Camacho '07, Harvey Mudd CollegeFollow
Robert D. Guy, University of California - Davis
Jon T. Jacobsen, Harvey Mudd CollegeFollow

Student Co-author

HMC Undergraduate

Document Type

Article

Department

Mathematics (HMC)

Publication Date

4-2008

Abstract

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.

Comments

This article is also available from the Society for Industrial and Applied Mathematics at http://dx.doi.org/10.1137/070687840.

Rights Information

© 2008 Society for Industrial and Applied Mathematics

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.1137/070687840

Recommended Citation

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.