Does a ‘volume‐filling effect’ always prevent chemotactic collapse?

By Michael Winkler. 2010

333 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Modeling and Simulation, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/06db8e76940d9d274a0b4471f2f170e5cc22ef03

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Citations in the corpus

A critical blow-up exponent in a chemotaxis system with nonlinear signal production (2018, background): “2033 solutions can be constructed [46], which in some cases are even known to blow-up in finite time [10–12].”
Global existence and boundedness in a Keller-Segel-Stokes model with arbitrary porous medium diffusion (2012, background): “Then known results say that solutions remain bounded whenever the (self-) difusivity D is large enough, as related to S, at large densities: Namely, if S(n) D(n) ≤ cn 2 N −ε holds for some c > 0, ε > 0 and all large n, then all solutions are global in time and bounded ([16], [22], [6], [9]), whereas”
Global classical solutions in a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity (2018, background): “6) then some solutions may become unbounded ([51], [24]), where in some particular cases and related systems involving nonlinear diffusion, such unboundedness phenomena are even known to occur within finite time ([8], [9]; cf.”
Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system (2011, background): “This type of reasoning, well-established in scalar parabolic problems ([25]) and also applicable in larger classes of quasilinear Keller-Segel models ([18], [19], [35]), evidently cannot give any information on the actual blow-up time, and hence cannot rule out the possibility that Tmax(u0, v0) = ∞.”
Boundedness of solutions to a quasilinear parabolic–elliptic Keller–Segel system with logistic source (2014, background): “1) with D 1 and g 0, the exponent 2 n also plays an important role: if q p < 2 n , the system exclusively possesses global bounded solutions [11], whereas if q p > 2 n with n 2, unbounded solutions do exist [9], and even finite-time blow-up may occur under the additional conditions n 3 and q 1 [12].”
Global existence and boundedness in a 3D Keller–Segel–Stokes system with nonlinear diffusion and rotational flux (2017, background): “In particular, for m = 1, all solutions are global and uniformly bounded if α > 1 − 2 d ([14,19]), while the solution may blow up if Ω ⊂ R (d ≥ 2) is a ball and α < 1 − 2 d under some technical assumptions ([14,37]).”