25 citations · 60 across the 11 of their papers we have counts for
12 papers
Orbital stability of undercompressive viscous shock waves under perturbation
Zhao Yang, Kevin Zumbrun
By the use of a new vertical estimate introduced by the authors in the context of relaxation shocks for shallow water flow, we both simplify and extend the basic stab…
Multidimensional stability and transverse bifurcation of hydraulic shocks and roll waves in open channel flow
Zhao Yang, Kevin Zumbrun
We study by a combination of analytical and numerical methods multidimensional stability and transverse bifurcation of planar hydraulic shock and roll wave solutions of the invisci…
Existence and stability of nonmonotone hydraulic shocks for the Saint Venant equations of inclined thin-film flow
Grégory Faye, L. Miguel Rodrigues, Zhao Yang +1
Extending work of Yang-Zumbrun for the hydrodynamically stable case of Froude number F < 2, we categorize completely the existence and convective stability of hydraulic shock profi…
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…
Asymptotic stability of sharp fronts: Analysis and rigorous computation
Blake Barker, Jared C. Bronski, Vera Mikyoung Hur +1
We investigate the stability of traveling front solutions to nonlinear diffusive-dispersive equations of Burgers type, with a primary focus on the Korteweg-de Vries-Burgers (KdVB)…
An alternative proof of modulation instability of Stokes waves in deep water
Zhao Yang
We generalize the periodic Evans function approach recently used to study the spectral stability of Stokes wave and gravity-capillary (including Wilton ripples) in water of finite…
Unstable Stokes waves
Vera Mikyoung Hur, Zhao Yang
We investigate the spectral instability of a periodic Stokes wave of sufficiently small amplitude, traveling in water of unit depth, under gravity. Numerical evidence sugges…
Stability of strong detonation waves for Majda's model with general ignition functions
Soyeun Jung, Zhao Yang, Kevin Zumbrun
For strong detonation waves of the inviscid Majda model, spectral stability was established by Jung and Yao for waves with step-type ignition functions, by a proof based largely on…
Spectral stability of hydraulic shock profiles
Alim Sukhtayev, Zhao Yang, Kevin Zumbrun
By reduction to a generalized Sturm Liouville problem, we establish spectral stability of hydraulic shock profiles of the Saint-Venant equations for inclined shallow-water flow, ov…
Stability of hydraulic shock profiles
Zhao Yang, Kevin Zumbrun
We establish nonlinear stability with sharp rates of decay in , , of general hydraulic shock profiles, with or without subshocks, of the invisci…
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…
Convergence as period goes to infinity of spectra of periodic traveling waves toward essential spectra of a homoclinic limit
Zhao Yang, Kevin Zumbrun
We revisit the analysis by R.A. Gardner of convergence of spectra of periodic traveling waves in the homoclinic, or infinite-period limit, extending his results to the case of esse…