The simple chemostat with wall growth

A model of the simple chemostat which allows for growth on the wall (or oth er marked surface) is presented as three nonlinear ordinary differential eq uations. The organisms which are attached to the wall do not wash out of th e chemostat. This destroys the basic reduction of the chemostat equations t o a monotone system, a technique which has been useful in the analysis of m any chemostat-like equations. The adherence to and shearing from the wall e liminates the boundary equilibria. For a reasonably general model, the basi c properties of invariance, dissipation, and uniform persistence are establ ished. For two important special cases, global asymptotic results are obtai ned. Finally, a perturbation technique allows the special results to be ext ended to provide the rest point as a global attractor for nearby growth fun ctions.