71 citations · 460 across the 61 of their papers we have counts for
7 papers · 2 filters
A stationary free boundary problem modeling electrostatic MEMS
Philippe Laurencot, Christoph Walker
A free boundary problem describing small deformations in a membrane based model of electrostatically actuated MEMS is investigated. The existence of stationary solutions is establi…
A gradient flow approach to a thin film approximation of the Muskat problem
Philippe Laurencot, Bogdan-Vasile Matioc
A fully coupled system of two second-order parabolic degenerate equations arising as a thin film approximation to the Muskat problem is interpreted as a gradient flow for the 2-Was…
Weak solutions to a thin film model with capillary effects and insoluble surfactant
Joachim Escher, Matthieu Hillairet, Philippe Laurencot +1
The paper focuses on a model describing the spreading of an insoluble surfactant on a thin viscous film with capillary effects taken into account. The governing equation for the fi…
Existence and uniqueness of very singular solutions for a fast diffusion equation with gradient absorption
Razvan Gabriel Iagar, Philippe Laurencot
Existence and uniqueness of radially symmetric self-similar very singular solutions are proved for the singular diffusion equation with gradient absorption {equation*} \partial_t u…
Positivity, decay, and extinction for a singular diffusion equation with gradient absorption
Razvan Gabriel Iagar, Philippe Laurencot
We study qualitative properties of non-negative solutions to the Cauchy problem for the fast diffusion equation with gradient absorption \partial_t u -Δ_{p}u+|\nabla u|^{q}=0\quad…
Weak solutions to the continuous coagulation equation with multiple fragmentation
Ankik Kumar Giri, Philippe Laurencot, Gerald Warnecke
The existence of weak solutions to the continuous coagulation equation with multiple fragmentation is shown for a class of unbounded coagulation and fragmentation kernels, the frag…
Existence and stability of weak solutions for a degenerate parabolic system modelling two-phase flows in porous media
Joachim Escher, Philippe Laurencot, Bogdan-Vasile Matioc
We prove global existence of nonnegative weak solutions to a degenerate parabolic system which models the interaction of two thin fluid films in a porous medium. Furthermore, we sh…