On a mathematical model for body tissue inflammation
A mathematical analysis is made of a model of inflammatory response to bacterial invasion of body tissue proposed by \textit{D. A. Lauffenburger} and \textit{C. R. Kennedy} [ibid. 16, 141-163 (1983; Zbl 0537.92007)]. The model is a system of two coupled nonlinear parabolic partial differential equations. A positivity theorem, an existence theorem and a uniqueness theorem are proved. The main part of the proof of the existence theorem is to establish the existence of a semiclassical solution (belonging to \(L^ 2\) and with derivatives in the Sobolev sense) by obtaining a priori estimates and then using the Leray-Schauder method.
inflammatory response to bacterial invasion of body tissue
system of two coupled nonlinear parabolic partial differential equations
scientific article; zbMATH DE number 4202082