We are interested in the thin-film equation with zero-contact angle and quadratic mobility,
modeling the spreading of a thin liquid film, driven by capillarity and limited by viscosity in …

Fluid films spreading on hydrophobic solid surfaces exhibit complicated dynamics that
describe transitions leading the films to break up into droplets. For viscous fluids coating …

We consider a degenerate nonlocal parabolic equation in a one-dimensional domain
introduced to model hydraulic fractures. The nonlocal operator is given by a fractional power …

We investigate compactly supported solutions for a thin-film equation with linear mobility in
the regime of perfect wetting. This problem has already been addressed by Carrillo and …

In any number of space variables, we study the Cauchy problem related to the fourth-order
degenerate diffusion equation∂ s h+∇⋅(h∇ Δ h)= 0. This equation, derived from a …

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 study well-posedness and regularity of the multidimensional thin-film equation with
linear mobility in a neighborhood of the self-similar Smyth–Hill solutions. To be more …

We establish well-posedness for the family of thin-film equations 1\left {h_t+(h^ n h_ xxx)
_x\=\0\quad {\rm in\h> 0\},\h\=\0, ‖ h_x|\=\1\quad\rm on\partial {h> 0\}. ht+(hnhxxx) x= 0 in h> …

We investigate perturbations of traveling-wave solutions to a thin-film equation with
quadratic mobility and a zero contact angle at the triple junction, where the three phases …

We consider the incompressible and stationary Stokes equations on an infinite two-
dimensional wedge with non-scaling invariant Navier-slip boundary conditions. We prove …