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 …

Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in
Mechanics and Physics is the first book to provide a systematic construction of exact …

We construct a continuum model for biological aggregations in which individuals experience
long-range social attraction and short-range dispersal. For the case of one spatial …

This paper is concerned with mathematical aspects of lubrication equations. In the first part,
we discuss recent analytical achievements for various types of thin-film equations. Of interest …

Alternating Direction Implicit (ADI) schemes are constructed for the solution of two-
dimensional higher-order linear and nonlinear diffusion equations, particularly including the …

We consider a thin film consisting of two layers of immiscible liquids on a solid horizontal
(heated) substrate. Both the free liquid–liquid and the liquid–gas interface of such a bilayer …

Lubrication theory for unstable thin liquid films on solid substrates is used to model the
coarsening dynamics in the long-time behavior of dewetting films. The dominant physical …

We study the influence of thermal fluctuations on the dewetting dynamics of thin liquid films.
Starting from the incompressible Navier-Stokes equations with thermal noise, we derive a …

The behavior of a thin liquid film on a uniformly heated substrate is considered. When the
substrate is horizontal and the Marangoni number sufficiently large the film breaks up into a …

We study the dewetting process of a thin liquid film on a chemically patterned solid substrate
(template) by means of a thin-film evolution equation incorporating a space-dependent …