On the weakly competitive case in a two-species chemotaxis model

By Tobias Black, Johannes Lankeit, M. Mizukami. 2016

108 citations recorded by the source corpus.

In this article we investigate a parabolic-parabolic-elliptic two-species chemotaxis system with weak competition and show global asymptotic stability of the coexistence steady state under a smallness condition on the chemotactic strengths, which seems more natural than the condition previously known. For the proof we rely on the method of eventual comparison, which thereby is shown to be a useful tool even in the presence of chemotactic terms.

Subfields: Modeling and Simulation, Molecular Biology, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/b223bd758f6b705c48a43436fbcfd43c6ff67fc6

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Citations in the corpus

Finite-time blow-up in low-dimensional Keller–Segel systems with logistic-type superlinear degradation (2018, background): “Indeed, the analysis on qualitative aspects of solution behavior in chemotaxis systems with logistic kinetics seems widely dominated by studies concerned with effects already known from the corresponding taxis-free and hence diagnonal reaction-diffusion systems; accordingly available findings on asy”
Large time behavior in the logistic Keller-Segel model via maximal Sobolev regularity (2017, background): “In the case τ = 0, the results from [10, 12, 2] can be summarized as: if the quotient χ μ is suitably small, (1) admits a global classical solution and it converges to ( κ μ , κ μ ).”