107 citations · 1.1k across the 120 of their papers we have counts for
133 papers
Linear damping estimates for periodic roll wave solutions of the inviscid Saint-Venant equations and related systems of hyperbolic balance laws
L. Miguel Rodrigues, Kevin Zumbrun
Substantially extending previous results of the authors for smooth solutions in the viscous case, we develop linear damping estimates for periodic roll-wave solutions of the invisc…
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…
Pseudodifferential damping estimates and stability of relaxation shocks
Kevin Zumbrun
A bottleneck in the theory of large-amplitude and multi-d viscous and relaxation shock stability is the development of nonlinear damping estimates controlling higher by lower deriv…
Linear stability analysis for a system of singular amplitude equations arising in biomorphology
Aric Wheeler, Kevin Zumbrun
We study linear stability of exponential periodic solutions of a system of singular amplitude equations associated with convective Turing bifurcation in the presence of conservatio…
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…