107 citations · 1.1k across the 120 of their papers we have counts for
11 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…
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…
High-frequency asymptotics and 1-D stability of ZND detonations in the small-heat release and high-overdrive limits
Kevin Zumbrun
We establish one-dimensional spectral, or "normal modes", stability of ZND detonations in the small heat release limit and the related high overdrive limit with heat release and ac…
Metastability of solitary roll wave solutions of the St. Venant equations with viscosity
Blake Barker, Mathew A. Johnson, L. Miguel Rodrigues +1
We study by a combination of numerical and analytical Evans function techniques the stability of solitary wave solutions of the St. Venant equations for viscous shallow-water flow…
Existence and stability of viscoelastic shock profiles
Blake Barker, Marta Lewicka, Kevin Zumbrun
We investigate existence and stability of viscoelastic shock profiles for a class of planar models including the incompressible shear case studied by Antman and Malek-Madani. We es…
Existence and stability of steady states of a reaction convection diffusion equation modeling microtubule formation
Shantia Yarahmadian, Blake Barker, Kevin Zumbrun +1
We generalize the Dogterom-Leibler model for microtubule dynamics [DL] to the case where the rates of elongation as well as the lifetimes of the elongating and shortening phases ar…