8 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,…
A potential theory approach to the capillarity-driven Hele-Shaw problem
Bogdan-Vasile Matioc, Christoph Walker
In this paper, we demonstrate that potential theory provides a powerful framework for analyzing quasistationary fluid flows in bounded geometries, where the bulk dynamics are gover…
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…
Linearized Stability of Non-Isolated Equilibria of Quasilinear Parabolic Problems in Interpolation Spaces
Bogdan-Vasile Matioc, Christoph Walker
The stability of non-isolated equilibria to quasilinear parabolic problems of the form is established in interpolation spaces (and thus extending previous resul…
Dynamics of the reversible Gray-Scott model and convergence to its irreversible limit
Philippe Laurençot, Christoph Walker
Well-posedness of a reversible variant of the Gray-Scott model is shown, along with the convergence of each trajectory to one of the two spatially homogeneous steady states. The pr…
On the principle of linearized stability for quasilinear evolution equations in time-weighted spaces
Bogdan-Vasile Matioc, Lina Sophie Schmitz, Christoph Walker
Quasilinear (and semilinear) parabolic problems of the form with strict inclusion of the domains of the function $v\maps…