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 propose a theory of weakly nonlinear multidimensional self-sustained detonations
based on asymptotic analysis of the reactive compressible Navier–Stokes equations. We …

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 …

High-speed deflagrations have burning velocities much higher than laminar ones, and
compressible effects become important. In the present paper, we study the structure of such …

We carry out the first rigorous numerical proof based on Evans function computations of
stability of viscous shock profiles, for the system of isentropic gas dynamics with monatomic …

The paper is concerned with the propagation of ion-acoustic shock waves in a collision
dominated plasma whose equations of motion are described by the one-dimensional …

Evans function computation is a useful tool in the study of asymptotically constant-coefficient
linear operators such as those found in the investigation of traveling wave stability. The roots …

The Evans function has been used extensively to study spectral stability of travelling-wave
solutions in spatially extended partial differential equations. To compute Evans functions …

Shock waves in reactive media possess very rich dynamics: from formation of cells in
multiple dimensions to oscillating shock fronts in one-dimension. Because of the extreme …

We describe recent analytical and numerical results on stability and behavior of viscous and
inviscid detonation waves obtained by dynamical systems/Evans function techniques like …