Related papers: Efficient numerical stability analysis of detonati…
We introduce a new method to investigate linear stability of gaseous detonations that is based on an accurate shock-fitting numerical integration of the linearized reactive Euler equations with a subsequent analysis of the computed solution…
Continuing the program initiated by Humpherys, Lyng, & Zumbrun [17] for strong detonation waves, we use a combination of analytical and numerical Evans-function techniques to analyze the spectral stability of weak detonation waves in a…
The rigorous study of spectral stability for strong detonations was begun by J.J. Erpenbeck in [Er1]. Working with the Zeldovitch-von Neumann-D\"oring (ZND) model, which assumes a finite reaction rate but ignores effects like viscosity…
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 those used to study shock and reaction diffusion waves. In…
Building on Evans function techniques developed to study the stability of viscous shocks, we examine the stability of viscous strong detonation wave solutions of the reacting Navier-Stokes equations. The primary result, following the work…
It has long been a standard practice to neglect diffusive effects in stability analyses of detonation waves. Here, with the principal aim of quantifying the impact of these oft-neglected effects on the stability characteristics of such…
Using Evans function techniques, we develop a stability index for weak and strong detonation waves analogous to that developed for shock waves in [GZ,BSZ], yielding useful necessary conditions for stability. Here, we carry out the analysis…
Using analytical and numerical Evans-function techniques, we examine the spectral stability of strong-detonation-wave solutions of Majda's scalar model for a reacting gas mixture with an Arrhenius-type ignition function. We introduce an…
The rigorous study of spectral stability of strong detonations was begun by Erpenbeck in the 1960s. Working with the Zeldovitch-von Neumann-D\"oring (ZND) model, he identified two fundamental classes of detonation profiles, referred to as…
In this work, we systematically generalize the Evans function methodology to address vector systems of discrete equations. We physically motivate and mathematically use as our case example a vector form of the discrete nonlinear Schrodinger…
We establish one-dimensional spectral, or "normal modes", stability of ZND detonations in the small heat release limit and the related high overdrive limit with heat release and activation energy held fixed, verifying numerical observations…
This paper is concerned with the stability of standing waves for the mass-critical Hartree equation with a focusing perturbation by the variational method. The profile decomposition theory is employed to prove the attainability of the cross…
We examine the spectral stability of travelling waves of the haptotaxis model studied in Harley et al (2014a). In the process we apply Li\'enard coordinates to the linearised stability problem and use a Riccati-transform/Grassmanian…
Extending recent results in the isentropic case, we use a combination of asymptotic ODE estimates and numerical Evans-function computations to examine the spectral stability of shock-wave solutions of the compressible Navier--Stokes…
The spectral problem associated with the linearization about solitary waves of spinor systems or optical coupled mode equations supporting gap solitons is formulated in terms of the Evans function, a complex analytic function whose zeros…
Frequently encountered in nature, internal solitary waves in stratified fluids are well-observed and well-studied from the experimental, the theoretical, and the numerical perspective. From the mathematical point of view, these waves are…
We carry out a systematic numerical stability analysis of ZND detonations of Majda's model with Arrhenius-type ignition function, a simplified model for reacting flow, as heat release and activation energy are varied. Our purpose is, first,…
For strong detonation waves of the inviscid Majda model, spectral stability was established by Jung and Yao for waves with step-type ignition functions, by a proof based largely on explicit knowledge of wave profiles. In the present work,…
We consider linear instability of solitary waves of several classes of dispersive long wave models. They include generalizations of KDV, BBM, regularized Boussinesq equations, with general dispersive operators and nonlinear terms. We obtain…
We consider the numerical evaluation of the Evans function, a Wronskian-like determinant that arises in the study of the stability of travelling waves. Constructing the Evans function involves matching the solutions of a linear ordinary…