Finite-time blow-up in a quasilinear system of chemotaxis

By Tomasz Cieślak, Michael Winkler. 2008

273 citations recorded by the source corpus.

Subfields: Cancer Research, Modeling and Simulation, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/08952a82d7a597c75a9ca438fb564e4d80539b34

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In Cancer Research

In Modeling and Simulation

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Citations in the corpus

On a parabolic–elliptic system with gradient dependent chemotactic coefficient (2018, background): “In the last years, linear diffusion of the biological especies ”u” has been replaced in different ways: • by nonlinear diffusion at the form −div(φ(u)∇u), see for instance Wrzosek [39], Cieslak and Mortales-Rodrigo [16], Cieslak and Winkler [17], Winkler [38].”
Critical mass for infinite-time aggregation in a chemotaxis model with indirect signal production (2016, unknown): “[34], [21], [18] and [8], for instance).”
Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity (2011, background): “the parabolic-parabolic case if D(u) ≃ u−γ and S(u) ≃ uα for large u with some γ ≥ 0 and α ∈ R: Solutions remain bounded if α + γ < 2 n, whereas blow-up may occur if α + γ > 2 n ([DW], cf. also [CW] for a precedent addresing the special case S(u) = u). Moreover, if S(u) = u, then even the crit”
Blow-up in a higher-dimensional chemotaxis system despite logistic growth restriction (2011, background): “to [3], [28] and [11] for detailed reasonings in closely related situations.”
Boundedness in a quasilinear fully parabolic Keller-Segel system of higher dimension with logistic source (2015, background): “Beyond this, more general functions φ and ψ are involved to denote the diffusivity and chemotatic sensitivity, respectively [5, 10, 22].”
Boundedness vs.blow-up in a two-species chemotaxis system with two chemicals (2015, unknown): “[7] and [34], for instance).”
Global Large-Data Solutions in a Chemotaxis-(Navier–)Stokes System Modeling Cellular Swimming in Fluid Drops (2012, background): “1), so that solutions should more likely remain bounded and hence be global in time; in fact, heuristic arguments of this type could be rigorously justified for Keller-Segel systems without fluid interaction (see [1, 18, 20], for instance).”