50 citations · 172 across the 48 of their papers we have counts for
7 papers · 2 filters
Positive solutions of some parabolic system with cross-diffusion and nonlocal initial conditions
Christoph Walker
The paper is concerned with a system consisting of two coupled nonlinear parabolic equations with a cross-diffusion term, where the solutions at positive times define the initial s…
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…
Bifurcation of Positive Equilibria in Nonlinear Structured Population Models with Varying Mortality Rates
Christoph Walker
A parameter-dependent model involving nonlinear diffusion for an age-structured population is studied. The parameter measures the intensity of the mortality. A bifurcation approach…
Coexistence Steady States in a Predator-Prey Model
Christoph Walker
An age-structured predator-prey system with diffusion and Holling-Tanner-type nonlinearities is considered. Regarding the intensity of the fertility of the predator as bifurcation…