In recent years, the Evans function has become an important tool for the determination of
stability of travelling waves. This function, a Wronskian of decaying solutions of the …

We establish nonlinear L 1∩ H 3→ L p orbital stability, 2≦ p≤∞, with sharp rates of decay,
of large-amplitude Lax-type shock profiles for a class of symmetric hyperbolic-parabolic …

We establish nonlinear stability and asymptotic behavior of traveling periodic waves of
viscous conservation laws under localized perturbations or nonlocalized perturbations …

In this paper we investigate the asymptotic stability of a composite wave consisting of two
viscous shock waves for the full compressible Navier-Stokes equation. By introducing a new …

In Evans function computations of the spectra of asymptotically constant-coefficient linear
operators, a basic issue is the efficient and numerically stable computation of subspaces …

We extend the Kreiss–Majda theory of stability of hyperbolic initial–boundary-value and
shock problems to a class of systems, notably including the equations of …

Abstract Extending results of Humpherys–Lyng–Zumbrun in the one-dimensional case, we
use a combination of asymptotic ODE estimates and numerical Evans-function computations …

Extending previous results of Oh–Zumbrun and Johnson–Zumbrun, we show that spectral
stability implies linearized and nonlinear stability of spatially periodic traveling wave …

Combining pointwise Green's function bounds obtained in a companion paper [36] with
earlier, spectral stability results obtained in [16], we establish nonlinear orbital stability of …

We establish existence and stability of multidimensional shock fronts in the vanishing
viscosity limit for a general class of conservation laws with “real”, or partially parabolic …