We highlight some recent developments that widen the scope and reach of mesoscopic thin-
film (or long-wave) hydrodynamic models employed to describe the dynamics of thin films …

This chapter illustrates how to apply continuation techniques in the analysis of a particular
class of nonlinear kinetic equations that describe the time evolution of a single scalar field …

We investigate the entrainment of liquid films on a partially wetting plate vertically withdrawn
from a reservoir of viscous liquid using a combination of diffuse-interface numerical …

We study fully three-dimensional droplets that slide down an incline by employing a thin-film
equation that accounts for capillarity, wettability, and a lateral driving force in small-gradient …

We briefly review selected mathematical models that describe the dynamics of pattern
formation phenomena in dip-coating and Langmuir-Blodgett transfer experiments, where …

We discuss the behavior of partially wetting liquids on a rotating cylinder using a model that
takes into account the effects of gravity, viscosity, rotation, surface tension, and wettability …

We study theoretically the mechanisms of square wave formation of a vertically emitting
micro-cavity operated in the Gires–Tournois regime that contains a Kerr medium and that is …

Liquid films can be entrained when the dewetting velocity attains a threshold, and this
dynamical wetting transition has been well studied in the situation of plane substrates. We …

We explore the bifurcation structure of a modified Cahn–Hilliard equation that describes a
system that may undergo a first-order phase transition and is kept permanently out of …

We present a brief comparative investigation of the bifurcation structure related to the
formation of two-dimensional deposition patterns as described by continuum models of …