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Heterogeneous dielectric properties in MEMS models
Philippe Laurencot, Christoph Walker
An idealized electrostatically actuated microelectromechanical system (MEMS) involving an elastic plate with a heterogeneous dielectric material is considered. Starting from the el…
Finite time singularity in a MEMS model revisited
Philippe Laurençot, Christoph Walker
A free boundary problem modeling a microelectromechanical system (MEMS) consisting of a fixed ground plate and a deformable top plate is considered, the plates being held at differ…
On a three-dimensional free boundary problem modeling electrostatic mems
Philippe Laurencot, Christoph Walker
We consider the dynamics of an electrostatically actuated thin elastic plate being clamped at its boundary above a rigid plate. The model includes the harmonic electrostatic potent…
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…
Sign-Preserving Property for Some Fourth-Order Elliptic Operators in One Dimension and Radial Symmetry
Philippe Laurencot, Christoph Walker
For a class of one-dimensional linear elliptic fourth-order equations with homogeneous Dirichlet boundary conditions it is shown that a non-positive and non-vanishing right-hand si…