50 citations · 51 across the 4 of their papers we have counts for
4 papers
Non-linear stability of shock profiles in dissipative hyperbolic-hyperbolic systems
Matthias Sroczinski, Kevin Zumbrun
We give the first proof of nonlinear stability for smooth shock profiles of second-order dissipative hyperbolic-hyperbolic systems under the assumption of spectral stability, showi…
Euler vs. Lagrange: The role of coordinates in practical Evans-function computations
Blake Barker, Jeffrey Humpherys, Gregory Lyng +1
The Evans function has become a standard tool in the mathematical study of nonlinear wave stability. In particular, computation of its zero set gives a convenient numerical method…
Stability of isentropic viscous shock profiles in the high-Mach number limit
Jeffrey Humpherys, Olivier Laffite, Kevin Zumbrun
By a combination of asymptotic ODE estimates and numerical Evans function calculations, we establish stability of viscous shock solutions of the isentropic compressible Navier--Sto…
An Evans function approach to spectral stability of small-amplitude shock profiles
Ramon Plaza, Kevin Zumbrun
We establish one-dimensional spectral stability of small amplitude viscous and relaxation shock profiles using Evans function techniques to perform a series of reductions and norma…