107 citations · 1.1k across the 120 of their papers we have counts for
12 papers · 2 filters
Transition to longitudinal instability of detonation waves is generically associated with Hopf bifurcation to time-periodic galloping solutions
Benjamin Texier, Kevin Zumbrun
We show that transition to longitudinal instability of strong detonation solutions of reactive compressible Navier--Stokes equations is generically associated with Hopf bifurcation…
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…
Nonlinear stability of time-periodic viscous shocks
Margaret Beck, Bjorn Sandstede, Kevin Zumbrun
In order to understand the nonlinear stability of many types of time-periodic travelling waves on unbounded domains, one must overcome two main difficulties: the presence of embedd…
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…
Existence and stability of noncharacteristic boundary-layers for the compressible Navier-Stokes and viscous MHD equations
Olivier Gues, Guy Metivier, Mark Williams +1
For a general class of hyperbolic-parabolic systems including the compressible Navier-Stokes and compressible MHD equations, we prove existence and stability of noncharacteristic v…
Long-time stability of large-amplitude noncharacteristic boundary layers for hyperbolic--parabolic systems
Toan Nguyen, Kevin Zumbrun
Extending investigations of Yarahmadian and Zumbrun in the strictly parabolic case, we study time-asymptotic stability of arbitrary (possibly large) amplitude noncharacteristic bou…
Spectral stability of weak relaxation shock profiles
Corrado Mascia, Kevin Zumbrun
Using a combination of Kawashima- and Goodman-type energy estimates, we establish spectral stability of general small-amplitude relaxation shocks of symmetric dissipative systems.…
Derivatives of (Modified) Fredholm Determinants and Stability of Standing and Traveling Waves
Fritz Gesztesy, Yuri Latushkin, Kevin Zumbrun
Continuing a line of investigation initiated in [11] exploring the connections between Jost and Evans functions and (modified) Fredholm determinants of Birman-Schwinger type integr…
Pointwise Green function bounds and long-time stability of large-amplitude noncharacteristic boundary layers
Shantia Yarahmadian, Kevin Zumbrun
Using pointwise semigroup techniques of Zumbrun--Howard and Mascia--Zumbrun, we obtain sharp global pointwise Green function bounds for noncharacteristic boundary layers of arbitra…