After a brief overview of the 'moving contact-line problem'as it emerged and evolved as a
research topic, a 'litmus test'allowing one to assess adequacy of the mathematical models …

We consider the thin-film equation for a class of free boundary conditions modelling friction
at the contact line, as introduced by E and Ren. Our analysis focuses on formal long-time …

We prove well-posedness, partial regularity, and stability of a thin-film equation $ h_t+(m (h)
h_ {zzz}) _z= 0$ with general mobility $ m (h)= h^ n $ and mobility exponent $ n\in (1,\tfrac …

We study global minimizers of a functional modeling the free energy of thin liquid layers over
a solid substrate under the combined effect of surface, gravitational, and intermolecular …

We are interested in a complete characterization of the contact-line singularity of thin-film
flows for zero and nonzero contact angles. By treating the model problem of source-type self …

In this paper, we revisit a model for the contact line problem which has been proposed by
Shikhmurzaev (Int. J. Multiph. Flow 19 (4): 589–610,). In the first part, in addition to …

We study theoretically and numerically the bending-driven levelling of thin viscous films
within the lubrication approximation. We derive Green's function of the linearized thin-film …

We investigate the large time behavior of compactly supported smooth solutions for a one-
dimensional thin-film equation with linear mobility in the regime of partial wetting. We show …

In the regime of lubrication approximation, we look at spreading phenomena under the
action of singular potentials of the form P (h)≈ h 1-m as h→ 0+ with m> 1, modeling …

This paper is devoted to the asymptotic analysis of a thin film equation that describes the
evolution of a thin liquid droplet on a solid support driven by capillary forces. We propose an …