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Ordinary Differential Equations and Applied Dynamics Commons™
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Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
Traveling Waves And Shocks In A Viscoelastic Generalization Of Burgers' Equation, Victor Camacho '07, Robert D. Guy, Jon T. Jacobsen
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.