Displaying similar documents to “PDE models for chemotactic movements: Parabolic, hyperbolic and kinetic”

On Chemotaxis Models with Cell Population Interactions

Z. A. Wang (2010)

Mathematical Modelling of Natural Phenomena

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This paper extends the volume filling chemotaxis model [18, 26] by taking into account the cell population interactions. The extended chemotaxis models have nonlinear diffusion and chemotactic sensitivity depending on cell population density, which is a modification of the classical Keller-Segel model in which the diffusion and chemotactic sensitivity are constants (linear). The existence and boundedness of global solutions of these models are...

Chemotaxis models with a threshold cell density

Dariusz Wrzosek (2008)

Banach Center Publications

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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...

Mathematical models of tumor growth systems

Takashi Suzuki (2012)

Mathematica Bohemica

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We study a class of parabolic-ODE systems modeling tumor growth, its mathematical modeling and the global in time existence of the solution obtained by the method of Lyapunov functions.