23 citations · 97 across the 32 of their papers we have counts for
7 papers · 1 filter
Rigorous Justification of the Whitham Modulation Equations for the Generalized Korteweg-de Vries Equation
Mathew Johnson, Kevin Zumbrun
In this paper, we consider the spectral stability of spatially periodic traveling wave solutions of the generalized Korteweg-de Vries equation to long-wavelength perturbations. Spe…
Instantaneous shock location and one-dimensional nonlinear stability of viscous shock wave
Kevin Zumbrun
We illustrate in a simple setting the instantaneous shock tracking approach to stability of viscous conservation laws introduced by Howard, Mascia, and Zumbrun. This involves a cho…
Existence of quasilinear relaxation shock profiles
Guy Metivier, Benjamin Texier, Kevin Zumbrun
We establish existence with sharp rates of decay and distance from the Chapman--Enskog approximation of small-amplitude quasilinear relaxation shocks in the general case that the p…
Existence and sharp localization in velocity of small-amplitude Boltzmann shocks
Guy Metivier, Kevin Zumbrun
Using a weighted -contraction mapping argument based on the macro-micro decomposition of Liu and Yu, we give an elementary proof of existence, with sharp rates of decay and di…
Stability of detonations in the ZND limit
Kevin Zumbrun
Confirming a conjecture of Lyng--Raoofi--Texier--Zumbrun, we show that stability of strong detonation waves in the ZND, or small-viscosity, limit is equivalent to stability of the…
Stability of scalar radiative shock profiles
Corrado Lattanzio, Corrado Mascia, Ramon Plaza +2
This work establishes nonlinear orbital asymptotic stability of scalar radiative shock profiles, namely, traveling wave solutions to the simplified model system of radiating gas \c…