Global Existence for a Parabolic Chemotaxis Model with Prevention of Overcrowding

By Thomas Hillen, Kevin J. Painter. Advances in Applied Mathematics, 2001

363 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Molecular Biology, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/86c4bb3596668416ab6d81661de48b8247b094f3

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Citations in the corpus

Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity (2011, background): “in ﬁnite time ([HV]); if n ≥ 3 and Ω is a ball, then for all M > 0 there exist initial data with R Ω u0 = M such that the solution will become unbounded either in ﬁnite or inﬁnite time ([Wi2]). In [HP01] the authors analyze (0.1) upon the particular choices D(u) ≡ 1 and S(u) = u(1− u)+. This corr”
The one‐dimensional chemotaxis model: global existence and asymptotic profile (2004, methodology): “In Hillen and Painter a modi ed chemotaxis model is studied which accounts for volume lling e ects of particles which have nite volume.”
Chemotaxis-fluid coupled model for swimming bacteria with nonlinear diffusion: Global existence and asymptotic behavior (2010, neutral): “Other ways to model prevention of overcrowding can be found in [13, 5, 4].”
A user’s guide to PDE models for chemotaxis (2009, neutral): “By including further details of the signal transduction process, other forms of sensitivity dependence can be deduced: if co-operative binding occurs, then the concentration of bound receptors may more reasonably by described as a Hill function φ(v) = βv n αv n +1 ; the effects of internalisation of”
Asymptotic analysis of an advection-dominated chemotaxis model in multiple spatial dimensions (2008, background): “Since this inequality holds for arbitrary test functions ϕ(x,t), the assertion follows.”
Existence of solutions of the hyperbolic Keller-Segel model (2006, background): “It enters a general class of problems in the description of cells movement ([17, 23, 13, 14, 11, 12, 22, 5]).”
Stationary states of quadratic diffusion equations with long-range attraction (2011, result): “More refined results in a similar model derived in [28, 46] with cut-off density have been found in [14, 34].”
On the global existence of solutions to an aggregation model (2008, methodology): “For additional literature concerning the Keller-Segel models see Hillen and Painter [18], Nagai et al.”
Spatio-temporal chaos in a chemotaxis model (2011, methodology): “The merging process for r = 0 has been studied in detail by Schaaf [34], and for a related model in which χ is replaced by the density dependent form χ(1 − u/Umax) (see [29,35]).”
A Chemotaxis Model with Threshold Density and Degenerate Diffusion (2005, background): “As already mentioned, the well-posedness of (1)-(4) has been established in [2] [9] when D and h are related by (5) and D(r) ≥ δ > 0 for r ∈ [0] [1].”