10 papers
Stability of Equilibria in a Biofilm Reactor Model with Wall Attachment and Thermodynamic Growth Inhibition
Katerina Nik, Christoph Walker
The dynamics of a mathematical model for a chemostat-type reactor is investigated. The model describes the temporal evolution of suspended and wall-attached bacterial populations,…
Analysis of a Biofilm Model in a Continuously Stirred Tank Reactor with Wall Attachment
Katerina Nik, Christoph Walker
We investigate a mathematical model for a bacterial population in a continuously stirred tank reactor with wall attachment. The model couples a free-boundary value problem for subs…
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…
Existence results for a morphoelastic model
Elisa Davoli, Katerina Nik, Ulisse Stefanelli
We present some existence results for three-dimensional quasistatic morphoelasticity. The state of the growing body is described by its deformation and the underlying growth tensor…
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…