107 citations · 1.1k across the 120 of their papers we have counts for
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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…
-modified characteristic Fredholm determinants, Hill's method, and the periodic Evans function of Gardne
Kevin Zumbrun
Using the relation established by Johnson--Zumbrun between Hill's method of aproximating spectra of periodic-coefficient ordinary differential operators and a generalized periodic…
A numerical stability investigation of strong ZND detonations for Majda's model
Blake Barker, Kevin zumbrun
We carry out a systematic numerical stability analysis of ZND detonations of Majda's model with Arrhenius-type ignition function, a simplified model for reacting flow, as heat rele…
Efficient numerical stability analysis of detonation waves in ZND
Jeffrey Humpherys, Kevin Zumbrun
As described in the classic works of Lee--Stewart and Short--Stewart, the numerical evaluation of linear stability of planar detonation waves is a computationally intensive problem…
Convergence of Hill's method for nonselfadjoint operators
Mathew A. Johnson, Kevin Zumbrun
By the introduction of a generalized Evans function defined by an appropriate 2-modified Fredholm determinant, we give a simple proof of convergence in location and multiplicity of…
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…