107 citations · 1.1k across the 120 of their papers we have counts for
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Convex entropy, Hopf bifurcation, and viscous and inviscid shock stability
Blake Barker, Heinrich Freistühler, Kevin Zumbrun
We consider by a combination of analytical and numerical techniques some basic questions regarding the relations between inviscid and viscous stability and existence of a convex en…
Behavior of periodic solutions of viscous conservation laws under localized and nonlocalized perturbations
Mathew A. Johnson, Pascal Noble, L. Miguel Rodrigues +1
We establish nonlinear stability and asymptotic behavior of traveling periodic waves of viscous conservation laws under localized perturbations or nonlocalized perturbations asympt…
Viscous boundary layers in hyperbolic-parabolic systems with Neumann boundary conditions
Olivier Gues, Guy Metivier, Mark Williams +1
We initiate the study of noncharacteristic boundary layers in hyperbolic-parabolic problems with Neumann boundary conditions. More generally, we study boundary layers with mixed Di…
Quasi-gradient systems, modulational dichotomies, and stability of spatially periodic patterns
Alin Pogan, Arnd Scheel, Kevin Zumbrun
Extending the approach of Grillakis-Shatah-Strauss, Bronski-Johnson-Kapitula, and others for Hamiltonian systems, we explore relations between the constrained variational problem $…
Nonlinear modulational stability of periodic traveling-wave solutions of the generalized Kuramoto-Sivashinsky equation
Blake Barker, Mathew A. Johnson, Pascal Noble +2
In this paper we consider the spectral and nonlinear stability of periodic traveling wave solutions of a generalized Kuramoto-Sivashinsky equation. In particular, we resolve the lo…
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^…