64 citations · 68 across the 8 of their papers we have counts for
10 papers
Qualitative properties of solutions to a non-local free boundary problem modeling cell polarization
Anna Logioti, Barbara Niethammer, Matthias Röger +1
We consider a parabolic non-local free boundary problem that has been derived as a limit of a bulk-surface reaction-diffusion system which models cell polarization. The authors hav…
Analysis and numerical treatment of bulk-surface reaction-diffusion models of Gierer-Meinhardt type
Jan-Phillip Bäcker, Matthias Röger, Dmitri Kuzmin
We consider a Gierer-Meinhardt system on a surface coupled with a parabolic PDE in the bulk, the domain confined by this surface. Such a model was recently proposed and analyzed fo…
A new Diffuse-interface approximation of the Willmore flow
Andreas Rätz, Matthias Röger
Standard diffuse approximations of the Willmore flow often lead to intersecting phase boundaries that in many cases do not correspond to the intended sharp interface evolution. Her…
Minimising a relaxed Willmore functional for graphs subject to boundary conditions
Klaus Deckelnick, Hans-Christoph Grunau, Matthias Röger
For a bounded smooth domain in the plane and smooth boundary data we consider the minimisation of the Willmore functional for graphs subject to Dirichlet or Navier boundary conditi…
Confined structures of least bending energy
Stefan Müller, Matthias Röger
In this paper we study a constrained minimization problem for the Willmore functional. For prescribed surface area we consider smooth embeddings of the sphere into the unit ball. W…
Symmetry breaking in a bulk-surface reaction-diffusion model for signaling networks
Andreas Rätz, Matthias Röger
Signaling molecules play an important role for many cellular functions. We investigate here a general system of two membrane reaction-diffusion equations coupled to a diffusion equ…