71 citations · 460 across the 61 of their papers we have counts for
7 papers · 2 filters
Self-similarity in a thin film Muskat problem
Philippe Laurencot, Bogdan-Vasile Matioc
The large time behavior of non-negative weak solutions to a thin film approximation of the two-phase Muskat problem is studied. A classification of self-similar solutions is first…
A variational approach to a stationary free boundary problem modeling MEMS
Philippe Laurencot, Christoph Walker
A variational approach is employed to find stationary solutions to a free boundary problem modeling an idealized electrostatically actuated MEMS device made of an elastic plate coa…
Large time behavior for the fast diffusion equation with critical absorption
Said Benachour, Razvan Gabriel Iagar, Philippe Laurencot
We study the large time behavior of nonnegative solutions to the Cauchy problem for a fast diffusion equation with critical zero order absorption $$ \partial_{t}u-Δu^m+u^q=0 \quad…
A hybrid variational principle for the Keller-Segel system in
Adrien Blanchet, José A. Carrillo, David Kinderlehrer +3
We construct weak global in time solutions to the classical Keller-Segel system cell movement by chemotaxis in two dimensions when the total mass is below the well-known critical v…
Absence of gelation and self-similar behavior for a coagulation-fragmentation equation
Philippe Laurencot, Henry Van Roessel
The dynamics of a coagulation-fragmentation equation with multiplicative coagulation kernel and critical singular fragmentation is studied. In contrast to the coagulation equation,…
The time singular limit for a fourth-order damped wave equation for MEMS
Philippe Laurencot, Christoph Walker
We consider a free boundary problem modeling electrostatic microelectromechanical systems. The model consists of a fourth-order damped wave equation for the elastic plate displacem…
Bounded traveling waves for a thin film with gravity and insoluble surfactant
Joachim Escher, Matthieu Hillairet, Philippe Laurencot +1
Lubrication equations for a surfactant-driven flow of a thin layer of fluid are considered with a singular surfactant-dependent surface tension. It is shown that there exists a bou…