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 …

Extending results of Oh and Zumbrun and of Johnson and Zumbrun for parabolic
conservation laws, we show that spectral stability implies nonlinear stability for spatially …

In this paper, we establish the nonlinear orbital stability of the traveling wave solution of
deterministic and stochastic delayed reaction–diffusion equation. Employing the …

Confirming a conjecture of Lyng–Raoofi–Texier–Zumbrun, we show that stability of strong
detonation waves in the ZND, or small-viscosity, limit is equivalent to stability of the limiting …

Motivated by physical and numerical observations of time oscillatory “galloping”,“spinning”,
and “cellular” instabilities of detonation waves, we study Poincaré–Hopf bifurcation of …

We show that transition to longitudinal instability of strong detonation solutions of reactive
compressible Navier–Stokes equations is generically associated with Hopf bifurcation to …

We study by a combination of numerical and analytical Evans function techniques, the
stability of solitary wave solutions of the St. Venant equations for viscous shallow water flow …

We illustrate in a simple setting the instantaneous shock tracking approach to stability of
viscous conservation laws introduced by Howard, Mascia, and Zumbrun. This involves a …

Extending our previous results for artificial viscosity systems, we show, under suitable
spectral hypotheses, that shock wave solutions of compressible Navier–Stokes and …

We investigate existence and stability of viscoelastic shock profiles for a class of planar
models including the incompressible shear case studied by Antman and Malek-Madani. We …