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16 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…
Transition between linear and exponential propagation in Fisher-KPP type reaction-diffusion equations
Anne-Charline Coulon, Jean-Michel Roquejoffre
We study the Fisher-KPP equation with a fractional laplacian of order α \in (0, 1). We know that the stable state invades the unstable one at constant speed for α = 1, and at an ex…
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…
Global Carleman estimates for waves and applications
Lucie Baudouin, Maya De Buhan, Sylvain Ervedoza
In this article, we extensively develop Carleman estimates for the wave equation and give some applications. We focus on the case of an observation of the flux on a part of the bou…
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…
Global existence for a hydrogen storage model with full energy balance
Elena Bonetti, Pierluigi Colli, Philippe Laurençot
A thermo-mechanical model describing hydrogen storage by use of metal hydrides has been recently proposed in a paper by Bonetti, Frémond and Lexcellent. It describes the formation…