Global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with strong logistic dampening

By Michael Winkler. 2014

300 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/282a49a3ebfbf83f64f91c5ac507a1308ecfe682

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Citations in the corpus

How strong a logistic damping can prevent blow-up for the minimal Keller–Segel chemotaxis system? (2016, unknown): “1) to the constant equilibrium (1/μ, 1/μ) as t → ∞ occurs [14, 34, 58].”
Blow-up prevention by quadratic degradation in a two-dimensional Keller–Segel–Navier–Stokes system (2016, background): “After all, at least for very large μ solutions of this system are known to stabilize toward spatially homogeneous equilibria whenever N ≥ 1 ([42]), and a similar behavior might be expected in (1.”
A three-dimensional Keller–Segel–Navier–Stokes system with logistic source: Global weak solutions and asymptotic stabilization (2019, background): “that even in the fluid-free case when u ≡ 0, this apparently provides some progress with regard to stabilization in the resulting logistic Keller-Segel system: For the latter, namely, though it has already been known that large values of μ χ enforce asymptotic stability of corresponding constant equ”
Very weak global solutions to a parabolic–parabolic chemotaxis-system with logistic source (2016, background): “The author proves that if μ is big enough, for all su ciently smooth and nonnegative initial data u0 and v0, the problem possesses a unique bounded and global-in-time classical solution (we also refer to [33] for more recent and speci c results).”
Attractiveness of Constant States in Logistic-Type Keller–Segel Systems Involving Subquadratic Growth Restrictions (2020, background): “In the best understood case α = 2 of quadratic absorption, for instance, associated no-flux initial-boundary value problems in n-dimensional bounded domainsΩ are known to admit global bounded classical solutions for all suitably regular initial data if either n ≤ 2 (see [26, 27]), or n ≥ 3 and μ > μ”
Boundedness in a two‐species chemotaxis system (2015, methodology): “In the high-dimensional case, we make use of the ideas in [19] to obtain the global solvability of (1.”