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1998 A nonlinear parabolic system modelling tissue inflammation
Philippe Laurençot, Didier Schmitt
Differential Integral Equations 11(4): 641-661 (1998). DOI: 10.57262/die/1367341038


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.


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Philippe Laurençot. Didier Schmitt. "A nonlinear parabolic system modelling tissue inflammation." Differential Integral Equations 11 (4) 641 - 661, 1998.


Published: 1998
First available in Project Euclid: 30 April 2013

zbMATH: 1005.92020
MathSciNet: MR1666210
Digital Object Identifier: 10.57262/die/1367341038

Primary: 92C50
Secondary: 35K57

Rights: Copyright © 1998 Khayyam Publishing, Inc.

Vol.11 • No. 4 • 1998
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