Dal Passo, R.; de Mottoni, P. On existence, uniqueness and attractivity of stationary solutions to some quasilinear parabolic systems. (English) Zbl 0572.35035 Mathematics in biology and medicine, Proc. Int. Conf., Bari/Italy 1983, Lect. Notes Biomath. 57, 482-487 (1985). [For the entire collection see Zbl 0559.00025.] The systems considered here are of the following form, solutions being \(u_ 1(x)\), \(u_ 2(x):\) \(\Delta \phi_ i(u_ 1,u_ 2)+f_ i(u_ 1,u_ 2)=0\) in \(\Omega\), \(i=1,2,\) with homogeneous Dirichlet conditions. First, results from the authors’ paper [Boll. Unione Mat. Ital., VI, Ser. C. Anal. Funz. Appl. 3, 203-231 (1984; Zbl 0552.35031)] are reviewed; they give conditions for existence, uniqueness, and global stability with reference to the corresponding parabolic systems. Then various examples are presented, representing models for the spread of infectious diseases. Reviewer: P.Fife Cited in 1 ReviewCited in 2 Documents MSC: 35J65 Nonlinear boundary value problems for linear elliptic equations 92D25 Population dynamics (general) 35B35 Stability in context of PDEs 35A05 General existence and uniqueness theorems (PDE) (MSC2000) Keywords:Dirichlet conditions; existence; uniqueness; global stability; spread of infectious diseases Citations:Zbl 0559.00025; Zbl 0552.35031 PDFBibTeX XML