4 papers · 1 filter
Dynamics of a free boundary problem with curvature modeling electrostatic MEMS
Joachim Escher, Philippe Laurencot, Christoph Walker
The dynamics of a free boundary problem for electrostatically actuated microelectromechanical systems (MEMS) is investigated. The model couples the electric potential to the deform…
On Nonlocal Parabolic Steady-State Equations of Cooperative or Competing Systems
Christoph Walker
Some systems of parabolic equations with nonlocal initial conditions are studied. The systems arise when considering steady-state solutions to diffusive age-structured cooperative…
Global weak solutions for a degenerate parabolic system modeling the spreading of insoluble surfactant
Joachim Escher, Matthieu Hillairet, Philippe Laurencot +1
We prove global existence of a nonnegative weak solution to a degenerate parabolic system, which models the spreading of insoluble surfactant on a thin liquid film.
On Positive Solutions of Some System of Reaction-Diffusion Equations with Nonlocal Initial Conditions
Christoph Walker
The paper focuses on positive solutions to a coupled system of parabolic equations with nonlocal initial conditions. Such equations arise as steady-state equations in an age-struct…