Singular limit in a model of tissue inflammation

Abstract.

A nonlinear parabolic system derived by Alt and Lauffenburger and modelling the inflammatory response of a one-dimensional tissue to a bacterial infection and including a chemotactic process is considered. For typical tissue widths the derivation of the model involves a small parameter $\epsilon$. The behaviour of the model as $\epsilon$ goes to zero is investigated and convergence of the solutions is obtained under rather weak requirements on the dependence of the initial data with respect to $\epsilon$.