64 citations · 349 across the 26 of their papers we have counts for
5 papers · 2 filters
Stability of Periodic Kuramoto-Sivashinsky Waves
Blake Barker, Mathew A. Johnson, Pascal Noble +2
In this note, we announce a general result resolving the long-standing question of nonlinear modulational stability, or stability with respect to localized perturbations, of period…
Modulated wave trains in generalized Kuramoto-Sivashinksi equations
Pascal Noble, Luis Miguel Rodrigues
This paper is concerned with the stability of periodic wave trains in a generalized Kuramoto-Sivashinski (gKS) equation. This equation is useful to describe the weak instability of…
Whitham's equations for modulated roll-waves in shallow flows
Pascal Noble, Luis Miguel Rodrigues
This paper is concerned with the detailed behaviour of roll-waves undergoing a low-frequency perturbation. We rst derive the so-called Whitham's averaged modulation equations and r…
Whitham Averaged Equations and Modulational Stability of Periodic Traveling Waves of a Hyperbolic-Parabolic Balance Law
Blake Barker, Mathew A. Johnson, Pascal Noble +2
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…
Nonlinear stability of viscous roll waves
Mathew Johnson, Kevin Zumbrun, Pascal Noble
Extending results of Oh--Zumbrun and Johnson--Zumbrun for parabolic conservation laws, we show that spectral stability implies nonlinear stability for spatially periodic viscous ro…