Chemotaxis models with a threshold cell density

Tom 81 / 2008

Dariusz Wrzosek Banach Center Publications 81 (2008), 553-566 MSC: Primary 35K55, 35K65; Secondary 34B15, 34C25. DOI: 10.4064/bc81-0-35


We consider a quasilinear parabolic system which has the structure of Patlak-Keller-Segel model of chemotaxis and contains a class of models with degenerate diffusion. A cell population is described in terms of volume fraction or density. In the latter case, it is assumed that there is a threshold value which the density of cells cannot exceed. Existence and uniqueness of solutions to the corresponding initial-boundary value problem and existence of space inhomogeneous stationary solutions are discussed. In the 1D case a classification of stationary solutions for some model example is provided.


  • Dariusz WrzosekInstitute of Applied Mathematics and Mechanics
    Warsaw University
    Banacha 2
    02-097 Warszawa, Poland

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