7 papers · 1 filter
A nonlocal transport problem describing pore growth
Barbara Niethammer, Lorena Pohl, Juan J. L. Velázquez
We study a nonlocal transport problem describing pore growth in a biological membrane exposed to a periodic electric potential, where the growth term is modified through the first…
Rigidity results for Euler flows in two dimensional exterior domains
Diego Alonso-Orán, Daniel Sánchez-Simón del Pino, Juan J. L. Velázquez
We study steady solutions of the two dimensional incompressible Euler equations in the exterior of a compact domain. We assume that fluid enters the exterior domain through every p…
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…
Mass concentration in a spatially inhomogeneous coagulation model with fast sedimentation
Iulia Cristian, Juan J. L. Velázquez
We study a spatially inhomogeneous coagulation model that contains a transport term in the spatial variable. The transport term models the vertical motion of particles due to gravi…
Rotating solutions to the incompressible Euler-Poisson equation with external particle
Diego Alonso-Orán, Bernhard Kepka, Juan J. L. Velázquez
We consider a two-dimensional, incompressible fluid body, together with self-induced interactions. The body is perturbed by an external particle with small mass. The whole configur…
On the Grad-Rubin boundary value problem for the two-dimensional magneto-hydrostatic equations
Diego Alonso-Orán, Juan J. L. Velázquez
In this work, we study the solvability of a boundary value problem for the magneto-hydrostatic equations originally proposed by Grad and Rubin in the late 50's. The proof relies on…