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Displaying similar documents to “Blow-up of solutions to a periodic nonlinear dispersive rod equation.”

Whitham averaged equations and modulational stability of periodic traveling waves of a hyperbolic-parabolic balance law

Blake Barker, Mathew A. Johnson, Pascal Noble, L.Miguel Rodrigues, Kevin Zumbrun (2010)

Journées Équations aux dérivées partielles

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In this note, we report on recent findings concerning the spectral and nonlinear stability of periodic traveling wave solutions of hyperbolic-parabolic systems of balance laws, as applied to the St. Venant equations of shallow water flow down an incline. We begin by introducing a natural set of spectral stability assumptions, motivated by considerations from the Whitham averaged equations, and outline the recent proof yielding nonlinear stability under these conditions. We then turn...