Differential and Integral Equations

A nonlinear parabolic system modelling tissue inflammation

Philippe Laurençot and Didier Schmitt

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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.

Article information

Differential Integral Equations, Volume 11, Number 4 (1998), 641-661.

First available in Project Euclid: 30 April 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 92C50: Medical applications (general)
Secondary: 35K57: Reaction-diffusion equations


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

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