Blow-up in a higher-dimensional chemotaxis system despite logistic growth restriction

By Michael Winkler. 2011

321 citations recorded by the source corpus.

Subfields: Cell Biology, Modeling and Simulation, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/e749afba3aaca0d81864bd983af65274bcc0e631

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Citations in the corpus

Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics (2016, background): “We mention that also subquadratic degradation may allow for global solvability in certain modified variants of the systems, provided that its effect is suitably relative to the aggregative mechanisms of cross-diffusion and signal production ([26], [27], [36]), but counterexamples show that not any s”
Dynamics in a parabolic-elliptic chemotaxis system with growth source and nonlinear secretion (2019, background): “However, the uniform boundedness of ‖u(t)‖L1 is not sufficient to prevent the blow-up of solutions in finite/infinite time (see [8, 26]).”
An attraction‐repulsion chemotaxis system with logistic source (2016, unknown): “Winkler [26] studied the system { ut = u − χ∇ · (u∇v) + λu − νu, 0 = v − m(t) + u (1.”
A critical blow-up exponent in a chemotaxis system with nonlinear signal production (2018, background): “Complementing results on the occurrence of blow-up solutions in three- and higher-dimensional domains, however, are available only in certain cases of subquadratic degradation, namely for κ < 32 + 1 2n−2 when n ≥ 5 ([49]), and alternatively for κ < 7 6 when n ∈ {3, 4} ([52]), thus yet leaving a cons”
Chemotaxis can prevent thresholds on population density (2014, background): “As [23] seems to indicate, superlinear absorption does not necessarily imply global existence.”
Global existence and asymptotic behavior of classical solutions to a parabolic-elliptic chemotaxis system with logistic source on $\mathbb{R}^{N}$ (2016, background): “The works [22], [46], [49] should be mentioned along this direction.”
A three-dimensional Keller–Segel–Navier–Stokes system with logistic source: Global weak solutions and asymptotic stabilization (2019, background): “2) with the death term −μn2 replaced by certain superlinear but subquadratic terms ([65]).”
Finite-time blow-up in low-dimensional Keller–Segel systems with logistic-type superlinear degradation (2018, background): “2), this provides progress in comparison to the results in ([44]) which, indeed, do not explicitly contain a density statement of the flavor in Corollary 1.”