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Chemotaxis models with a threshold cell density

100%
Wrzosek D.
Banach Center Publications
|
2008
|
tom 81
|
nr 1
553-566
EN
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.
2
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A nonlocal coagulation-fragmentation model

63%
Lachowicz M., Wrzosek D.
Applicationes Mathematicae
|
2000
|
tom 27
|
nr 1
45-66
EN
A new nonlocal discrete model of cluster coagulation and fragmentation is proposed. In the model the spatial structure of the processes is taken into account: the clusters may coalesce at a distance between their centers and may diffuse in the physical space Ω. The model is expressed in terms of an infinite system of integro-differential bilinear equations. We prove that some results known in the spatially homogeneous case can be extended to the nonlocal model. In contrast to the corresponding local models the analysis can be carried out in the $L_1(Ω)$ setting. Our purpose is to study global (in time) existence, mass conservation and well-posedness of the model.
3
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The Becker-Döring model with diffusion. I. Basic properties of solutions

63%
Laurençot P., Wrzosek D.
Colloquium Mathematicum
|
1998
|
tom 75
|
nr 2
245-269
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