Differential and Integral Equations
- Differential Integral Equations
- Volume 11, Number 4 (1998), 641-661.
A nonlinear parabolic system modelling tissue inflammation
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.
Differential Integral Equations, Volume 11, Number 4 (1998), 641-661.
First available in Project Euclid: 30 April 2013
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Laurençot, Philippe; Schmitt, Didier. A nonlinear parabolic system modelling tissue inflammation. Differential Integral Equations 11 (1998), no. 4, 641--661. https://projecteuclid.org/euclid.die/1367341038