23 citations · 109 across the 55 of their papers we have counts for
8 papers · 1 filter
Conditional stability of unstable viscous shocks
Kevin Zumbrun
Continuing a line of investigation initiated by Texier and Zumbrun on dynamics of viscous shock and detonation waves, we show that a linearly unstable Lax-type viscous shock soluti…
Center stable manifolds for quasilinear parabolic pde and conditional stability of nonclassical viscous shock waves
Kevin Zumbrun
Motivated by the study of conditional stability of traveling waves, we give an elementary center stable manifold construction for quasilinear parabolic PDE, sidestepping appa…
Stability and asymptotic behavior of periodic traveling wave solutions of viscous conservation laws in several dimensions
Myunghyun Oh, Kevin Zumbrun
Under natural spectral stability assumptions motivated by previous investigations of the associated spectral stability problem, we determine sharp estimates on the linearized…
Asymptotic Behavior of Multidimensional Scalar Relaxation Shocks
Bongsuk Kwon, Kevin Zumbrun
We establish pointwise bounds for the Green function and consequent linearized stability for multidimensional planar relaxation shocks of general relaxation systems whose equilibri…
Stability of noncharacteristic boundary layers in the standing shock limit
Kevin Zumbrun
We investigate one- and multi-dimensional stability of noncharacteristic boundary layers in the limit approaching a standing planar shock wave , , obtaining nec…
Long-time stability of multi-dimensional noncharacteristic viscous boundary layers
Toan Nguyen, Kevin Zumbrun
We establish long-time stability of multi-dimensional noncharacteristic boundary layers of a class of hyperbolic--parabolic systems including the compressible Navier--Stokes equati…