Volume-filling and quorum-sensing in models for chemosensitive movement

By Kevin J. Painter, Thomas Hillen. 2002

616 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/3838438e65876f2c05455281927adf6279c16f58

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Citations in the corpus

Global existence for chemotaxis with finite sampling radius (2006, methodology): “Such considerations led Othmer and Hillen [22] to propose the inclusion of a finite sampling radius in a model, as defined in (3).”
Global boundedness in a fully parabolic attraction–repulsion chemotaxis model (2015, background): “Moreover, there is an important mathematical difference between the classical Keller–Segel system and the attraction–repulsion model [10, 11] in the sense that the former exists a useful Lyapunov functional whereas the latter generally does not possess such a functional.”
Boundedness in the Higher-Dimensional Parabolic-Parabolic Chemotaxis System with Logistic Source (2010, background): “[ 18 ] or [ 19 ]), which in addition indicate that ( 0.”
Competing effects of attraction vs. repulsion in chemotaxis (2013, unknown): “However, in many biological processes, cells often interact with a combination of repulsive and attractive signaling chemicals to produce various interesting biological patterns.(8,12,16,39) This work aims to understand the competition between attractive and repulsive signals, and we consider the fo”
Asymptotic dynamics of the one‐dimensional attraction–repulsion Keller–Segel model (2015, methodology): “The Keller–Segel model with both attraction and repulsion was first proposed in [8] to describe the quorum effect in chemotaxis and in [9] to describe the aggregation of microglia in Alzheimer’s disease.”
Initial–boundary value problems for a system of hyperbolic balance laws arising from chemotaxis (2015, background): “which was developed in [23] to describe the aggregation of microglia observed in Alzheimer’s disease, and in [26] to study the quorum effect in chemotactic processes.”
A user’s guide to PDE models for chemotaxis (2009, unknown): “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”
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].”