We prove the existence of non-negative martingale solutions to a class of stochastic
degenerate-parabolic fourth-order PDEs arising in surface-tension driven thin-film flow …

We prove the existence of martingale solutions to stochastic thin-film equations in the
physically relevant space dimension d D 2. Conceptually, we rely on a stochastic Faedo …

This paper is concerned with the convergence to sharp traveling waves of solutions with
semi-compactly supported initial data for Burgers-Fisher-KPP equations with degenerate …

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 establish existence of nonnegative martingale solutions to stochastic thin-film equations
with quadratic mobility for compactly supported initial data under Stratonovich noise. Based …

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 …

Nonlinear partial differential equations admitting traveling wave solutions play an important
role in the description and analysis of real-life physical processes and nonlinear …

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

We consider the thin-film equation∂ t h+∇⋅(h 2∇ Δ h)= 0 in physical space dimensions (ie,
one dimension in time t and two lateral dimensions with h denoting the height of the film in …

We discuss a lubrication approximation model of the interface between two immiscible fluids
in a Hele-Shaw cell, derived in Constantin et al.(Phys Rev E 47 (6): 4169–4181, 1993) and …