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 study for the Richard–Gavrilyuk model of inclined shallow-water flow, an extension of the
classical Saint Venant equations incorporating vorticity, the new feature of convective-wave …

We study by a combination of analytical and numerical Evans function techniques multi-D
viscous and inviscid stability and associated transverse bifurcation of planar slow Lax MHD …

We treat the 1D shock tube problem, establishing existence of steady solutions of full
(nonisentropic) polytropic gas dynamics with arbitrary noncharacteristic data. We present …

The Evans function has become a standard tool in the mathematical study of nonlinear wave
stability. In particular, computation of its zero set gives a convenient numerical method for …

This thesis focuses on the study of spectral stability of planar shock waves in 2-dimensional
magnetohydrodynamics. We begin with a numerical approach, computing the Lopatinski …

Time evolution of initial data in Partial Differential Equations (PDEs) plays an important role
in understanding physical phenomena, and is of particular interest in determining the long …