41 citations · 275 across the 32 of their papers we have counts for
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Some thin film models based on Shikhmurzaev's approach
Amrita Ghosh, Barbara Niethammer, Juan J. L. Velazquez
We derive several lubrication approximation models, using Shikhmurzaev's approach to the contact line problem, obtained in \cite{GNV}. The first two lubrication models describe thi…
Revisiting Shikhmurzaev's approach to the contact line problem
Amrita Ghosh, Barbara Niethammer, Juan J. L. Velazquez
In this paper, we revisit a model for the contact line problem which has been proposed by Shikhmurzaev (1993). In the first part, in addition to rederiving the model, we study in d…
Analysis of a two-fluid Taylor-Couette flow with one non-Newtonian fluid
Christina Lienstromberg, Tania Pernas-Castaño, Juan J. L. Velázquez
We study the dynamic behaviour of two viscous fluid films confined between two concentric cylinders rotating at a small relative velocity. It is assumed that the fluids are immisci…
Two-speed solutions to non-convex rate-independent systems
Filip Rindler, Sebastian Schwarzacher, Juan J. L. Velazquez
We consider evolutionary PDE inclusions of the form \[ -λ\dot{u}_λ+ Δu - \mathrm{D} W_0(u) + f \ni \partial \mathcal{R}_1(\dot{u}) \qquad\text{in ,} \] where $\math…
Hopf Bifurcation in Structural Population Models
Narek Hovsepyan, Juan J. L. Velázquez
We study a nonlinear PDE problem motivated by the peculiar patterns arising in myxobacteria, namely counter-migrating cell density waves. We rigorously prove the existence of Hopf…
Homogenization for the Poisson equation in randomly perforated domains under minimal assumptions on the size of the holes
Arianna Giunti, Richard Höfer, Juan J. L. Velázquez
This paper deals with the homogenization of the Poisson equation in a bounded domain of , , which is perforated by a random number of small spherical holes with…