Christoph Walker

activity

20232026

collaborators

12 papers

math.AP2026

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,…

math.AP2026

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…

math.AP2026

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 $u^{'} = A (u) u + f (u)$ is established in interpolation spaces (and thus extending previous resul…

math.AP2025

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…

math.AP2025

Recovering Initial States in Certain Quasilinear Parabolic Problems from Time Averages

Bogdan-Vasile Matioc, Christoph Walker

The inverse problem of reconstructing the initial state in quasilinear parabolic equations from time averages is investigated. Under suitable regularity assumptions on the quasilin…

math.AP2025

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…

math.AP2024

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 $v^{'} = A (v) v + f (v)$ with strict inclusion $dom (f) ⊊ dom (A)$ of the domains of the function $v\maps…

math.AP2024

Quasilinear parabolic equations with superlinear nonlinearities in critical spaces

Bogdan-Vasile Matioc, Luigi Roberti, Christoph Walker

Well-posedness in time-weighted spaces for quasilinear (and semilinear) parabolic evolution equations $u^{'} = A (u) u + f (u)$ is established in a certain critical case of strict inclusion…

math.AP2024

Recovering Initial States in Semilinear Parabolic Problems from Time-Averages

Lina Sophie Schmitz, Christoph Walker

Well-posedness of certain semilinear parabolic problems with nonlocal initial conditions is shown in time-weighted spaces. The result is applied to recover the initial states in se…

math.AP2024

Global solutions for semilinear parabolic evolution problems with Hölder continuous nonlinearities

Bogdan-Vasile Matioc, Christoph Walker

It is shown that semilinear parabolic evolution equations $u^{'} = A + f (t, u)$ featuring Hölder continuous nonlinearities $f = f (t, u)$ with at most linear growth possess global strong solu…

math.AP2024

On a Quasilinear Parabolic-Hyperbolic System Arising in MEMS Modeling

Christoph Walker

A coupled system consisting of a quasilinear parabolic equation and a semilinear hyperbolic equation is considered. The problem arises as a small aspect ratio limit in the modeling…

math.AP2023

Well-Posedness of Quasilinear Parabolic Equations in Time-Weighted Spaces

Bogdan Matioc, Christoph Walker

Well-posedness in time-weighted spaces of certain quasilinear (and semilinear) parabolic evolution equations $u^{'} = A (u) u + f (u)$ is established. The focus lies on the case of strict in…