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Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

2008

Ordinary Differential Equations and Applied Dynamics

Claremont Colleges

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Traveling Waves And Shocks In A Viscoelastic Generalization Of Burgers' Equation, Victor Camacho '07, Robert D. Guy, Jon T. Jacobsen Apr 2008

Traveling Waves And Shocks In A Viscoelastic Generalization Of Burgers' Equation, Victor Camacho '07, Robert D. Guy, Jon T. Jacobsen

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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.

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