The dynamics and stability of thin liquid films have fascinated scientists over many decades:
the observations of regular wave patterns in film flows down a windowpane or along …

We summarize recent progress on one-dimensional and multidimensional stability of
viscous shock wave solutions of compressible Navier–Stokes equations and related …

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

The authors introduce two nonlinear advection-diffusion equations, each of which combines
Burgers's convection with a fourth order nonlinear diffusion previously designed for image …

We consider the stability of the steady free-surface thin-film flows over topography examined
in detail by Kalliadasis et al.(2000). For flow over a step-down, their computations revealed …

We consider undercompressive traveling wave solutions of the partial differential
equation\partial_t h+\partial_x f (h)=-\partial_x (h^ 3\partial_x^ 3 h)+ D\partial_x (h …

We provide a 'user guide'to the literature of the past twenty years concerning the modelling
and approximation of discontinuous solutions to nonlinear hyperbolic systems that admit …

Making use of detailed pointwise Green's function bounds obtained in a previous work for
the linearized equations about the wave, we give a straightforward derivation of the …

The Buckley–Leverett equation for two-phase flow in a porous medium is modified by
including dependence of the capillary pressure on the rate of change of saturation. This …

The goal of this article is to analyse the time asymptotic stability of one dimensional Bloch
wall in ferromagnetic materials. The equation involved in modelling such materials is the …