71 citations · 460 across the 61 of their papers we have counts for
5 papers · 2 filters
A parabolic free boundary problem modeling electrostatic MEMS
Joachim Escher, Philippe Laurencot, Christoph Walker
The evolution problem for a membrane based model of an electrostatically actuated microelectromechanical system (MEMS) is studied. The model describes the dynamics of the membrane…
A thin film approximation of the Muskat problem with gravity and capillary forces
Philippe Laurencot, Bogdan-Vasile Matioc
Existence of nonnegative weak solutions is shown for a thin film approximation of the Muskat problem with gravity and capillary forces taken into account. The model describes the s…
A phase-field approximation of the Willmore flow with volume and area constraints
Pierluigi Colli, Philippe Laurencot
The well-posedness of a phase-field approximation to the Willmore flow with area and volume constraints is established when the functional approximating the area has no critical po…
The parabolic-parabolic Keller-Segel system with critical diffusion as a gradient flow in $\RR^d$,
Adrien Blanchet, Philippe Laurençot
It is known that, for the parabolic-elliptic Keller-Segel system with critical porous-medium diffusion in dimension $\RR^d$, (also referred to as the quasilinear Smolucho…
Eternal solutions to a singular diffusion equation with critical gradient absorption
Razvan Gabriel Iagar, Philippe Laurencot
The existence of nonnegative radially symmetric eternal solutions of exponential self-similar type is investigated for the singular diffus…