We investigate the well-posedness of a nonlinear parabolic system modelling inflammation in a one-dimensional tissue; it describes the evolution of concentrations of bacteria and leukocytes, and includes a chemotactic process. We consider the case of bacterial infection occurring initially only at the tissue surface; the initial data for the concentration of bacteria is thus a Dirac mass at the boundary. Existence and uniqueness of the solution with such an initial data is proved. The main point is the uniqueness result, which is obtained by a duality argument.
"A nonlinear parabolic system modelling tissue inflammation." Differential Integral Equations 11 (4) 641 - 661, 1998.