Singular limit in a model of tissue inflammation (Q1288180)

The authors consider a nonlinear parabolic system which involves a small parameter \(\varepsilon\), and describe the inflammatory response of a one-dimensional tissue to a bacterial invasion, including a chemotactic mechanism [\textit{W. Alt}, \textit{D. A. Lauffenburger}, J. Math. Biol. 24, 691-722 (1987; Zbl 0609.92020)]. They study the convergence of the solution \((v^\varepsilon,w^\varepsilon,u^\varepsilon)\) as \(\varepsilon\to 0\). Their investigation is based on a priori estimates for \((v^\varepsilon, w^\varepsilon, u^\varepsilon)\) which hold uniformly with respect to \(\varepsilon\) in \(L^p\)-type spaces.