3 papers
math.AP2025
Analysis of a one-dimensional biofilm model
Patrick Guidotti, Christoph Walker
In this paper a reduced one-dimensional moving boundary model is studied that describes the evolution of a biofilm driven by the presence of a reaction limiting substrate. Global w…
math.AP2024
Analytic semigroups in weighted -spaces on the half-line generated by singular or degenerate operators
Patrick Guidotti, Philippe Laurençot, Christoph Walker
Ranges of the real-valued parameters , , , and are identified for which the operator $$\mathcal{A}_α(a,b)f(x):=x^α\left(f''(x)+\frac{a}{x}f'(x)+\frac{b}{x^2}f(x)\right…
math.AP2014
Bounded traveling waves for a thin film with gravity and insoluble surfactant
Joachim Escher, Matthieu Hillairet, Philippe Laurencot +1
Lubrication equations for a surfactant-driven flow of a thin layer of fluid are considered with a singular surfactant-dependent surface tension. It is shown that there exists a bou…