111 citations · 300 across the 44 of their papers we have counts for
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Localization properties of a free boundary problem for cell polarization
B. Niethammer, M. Röger, J. J. L. Velázquez
We investigate localization in a time-dependent contrained obstacle problem for the density of an active protein on a cell membrane. This free boundary problem has been derived in…
On the shape of the positivity region for a free boundary problem describing cell polarization
Sebastián Flores Sepúlveda, Barbara Niethammer, Juan J. L. Velázquez
In this paper we study a mass-constrained free boundary problem modeling cell polarization, in the regime where the mass is small. In the generic case of a signal with nondegenerat…
Long-time behaviour of a nonlocal model for electroporation
Barbara Niethammer, Lorena Pohl, Juan J. L. Velázquez
In this paper we analyze a model for electroporation, a biological process in which a cell membrane exposed to an external voltage becomes permeable due to the formation and growth…
A note on instantaneous gelation for coagulation kernels vanishing on the diagonal
Iulia Cristian, Barbara Niethammer, Juan J. L. Velázquez
We prove that instantaneous gelation (i.e., instantaneous loss of mass) occurs for coagulation equations with sum-type kernels of homogeneity greater than one which vanish on the d…
On an inhomogeneous coagulation model with a differential sedimentation kernel
Iulia Cristian, Barbara Niethammer, Juan J. L. Velázquez
We study an inhomogeneous coagulation equation that contains a transport term in the spatial variable modeling the sedimentation of clusters. We prove local existence of mass conse…
Interface behavior for the solutions of a mass conserving 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. In previous pap…