71 citations · 460 across the 61 of their papers we have counts for
8 papers · 2 filters
Weak solutions to lubrication equations in the presence of strong slippage
Georgy Kitavtsev, Philippe Laurencot, Barbara Niethammer
The existence of global weak solutions is proved for one-dimensional lubrication models that describe the dewetting process of nanoscopic thin polymer films on hydrophobyzed substr…
Global weak solutions for a degenerate parabolic system modeling the spreading of insoluble surfactant
Joachim Escher, Matthieu Hillairet, Philippe Laurencot +1
We prove global existence of a nonnegative weak solution to a degenerate parabolic system, which models the spreading of insoluble surfactant on a thin liquid film.
Global-in-time solutions for the isothermal Matovich-Pearson equations
Eduard Feireisl, Philippe Laurencot, Andro Mikelic
In this paper we study the Matovich-Pearson equations describing the process of glass fiber drawing. These equations may be viewed as a 1D-reduction of the incompressible Navier-St…
Convergence to separate variables solutions for a degenerate parabolic equation with gradient source
Philippe Laurencot, Christian Stinner
The large time behaviour of nonnegative solutions to a quasilinear degenerate diffusion equation with a source term depending solely on the gradient is investigated. After a suitab…
Refined asymptotics for the infinite heat equation with homogeneous Dirichlet boundary conditions
Philippe Laurencot, Christian Stinner
The nonnegative viscosity solutions to the infinite heat equation with homogeneous Dirichlet boundary conditions are shown to converge as time increases to infinity to a uniquely d…
A phase-field approximation of the Willmore flow with volume constraint
Pierluigi Colli, Philippe Laurençot
The well-posedness of a phase-field approximation to the Willmore flow with volume constraint is established. The existence proof relies on the underlying gradient flow structure o…
Thin Film Equations with Soluble Surfactant and Gravity: Modeling and Stability of Steady States
Joachim Escher, Matthieu Hillairet, Philippe Laurençot +1
A thin film on a horizontal solid substrate and coated with a soluble surfactant is considered. The governing degenerate parabolic equations for the film height and the surfactant…
Global existence vs. blowup for the one dimensional quasilinear Smoluchowski-Poisson system
Tomasz Cieslak, Philippe Laurencot
We prove that, unlike in several space dimensions, there is no critical (nonlinear) diffusion coefficient for which solutions to the one dimensional quasilinear Smoluchowski-Poisso…