25 citations · 25 across the 5 of their papers we have counts for
6 papers
Linear damping estimates for periodic roll wave solutions of the inviscid Saint-Venant equations and related systems of hyperbolic balance laws
L. Miguel Rodrigues, Kevin Zumbrun
Substantially extending previous results of the authors for smooth solutions in the viscous case, we develop linear damping estimates for periodic roll-wave solutions of the invisc…
Phase sinks and sources around two-dimensional periodic-wave solutions of reaction-diffusion-advection systems
Benjamin Melinand, L. Miguel Rodrigues
We develop a complete stability theory for two-dimensional periodic traveling waves of reaction-diffusion systems. More precisely, we identify a diffusive spectral stability assump…
Convective-wave solutions of the Richard-Gavrilyuk model for inclined shallow water flow
L. Miguel Rodrigues, Zhao Yang, Kevin Zumbrun
We study for the Richard-Gavrilyuk model of inclined shallow water flow, an extension of the classical Saint Venant equations incorporating vorticity, the new feature of convective…
Spectral Stability of Inviscid Roll Waves
Mathew A. Johnson, Pascal Noble, L. Miguel Rodrigues +2
We carry out a systematic analytical and numerical study of spectral stability of discontinuous roll wave solutions of the inviscid Saint Venant equations, based on a periodic Evan…
Note on the stability of viscous roll-waves
Blake Barker, Mathew A. Johnson, Pascal Noble +2
In this note, we announce a complete classification of stability of periodic roll-wave solutions of the viscous shallow-water equations, from their onset at Froude number $F\approx…
Spectral stability of periodic wave trains of the Korteweg-de Vries/Kuramoto-Sivashinsky equation in the Korteweg-de Vries limit
Mathew A. Johnson, Pascal Noble, L. Miguel Rodrigues +1
We study the spectral stability of a family of periodic wave trains of the Korteweg-de Vries/Kuramoto-Sivashinsky equation $ \partial_t v+v\partial_x v+\partial_x^3 v+δ(\partial_x^…