6 papers · 1 filter
Long-time behaviour and stability for quasilinear doubly degenerate parabolic equations of higher order
Jonas Jansen, Christina Lienstromberg, Katerina Nik
We study the long-time behaviour of solutions to quasilinear doubly degenerate parabolic problems of fourth order. The equations model for instance the dynamic behaviour of a non-N…
A direct construction of a full family of Whitham solitary waves
Mats Ehrnström, Katerina Nik, Christoph Walker
Starting with the periodic waves earlier constructed for the gravity Whitham equation, we parameterise the solution curves through relative wave height, and use a limiting argument…
On a Free Boundary Model for Three-Dimensional MEMS with a Hinged Top Plate II: Parabolic Case
Katerina Nik
A parabolic free boundary problem modeling a three-dimensional electrostatic MEMS device is investigated. The device is made of a rigid ground plate and an elastic top plate which…
On a Free Boundary Model for Three-Dimensional MEMS with a Hinged Top Plate I: Stationary Case
Katerina Nik
A stationary free boundary problem modeling a three-dimensional electrostatic MEMS device is investigated. The device is made of a rigid ground plate and an elastic top plate which…
Convergence of energy minimizers of a MEMS model in the reinforced limit
Philippe Laurençot, Katerina Nik, Christoph Walker
Energy minimizers to a MEMS model with an insulating layer are shown to converge in its reinforced limit to the minimizer of the limiting model as the thickness of the layer tends…
Energy minimizers for an asymptotic MEMS model with heterogeneous dielectric properties
Philippe Laurençot, Katerina Nik, Christoph Walker
A model for a MEMS device, consisting of a fixed bottom plate and an elastic plate, is studied. It was derived in a previous work as a reinforced limit when the thickness of the in…