Delayed blow‐up for chemotaxis models with local sensing

By Martin Burger, Philippe Laurençot, Ariane Trescases. Journal of the London Mathematical Society, 2020

61 citations recorded by the source corpus.

The aim of this paper is to analyze a model for chemotaxis based on a local sensing mechanism instead of the gradient sensing mechanism used in the celebrated minimal Keller–Segel model. The model we study has the same entropy as the minimal Keller–Segel model, but a different dynamics to minimize this entropy. Consequently, the conditions on the mass for the existence of stationary solutions or blow‐up are the same; however, we make the interesting observation that with the local sensing mechanism the blow‐up in the case of supercritical mass is delayed to infinite time.

Subfields: Modeling and Simulation, Molecular Biology, Oncology

View Paper: https://www.semanticscholar.org/paper/1dd44bf059bcd24fb9dac28fd88bb7d785c9e240

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Citations in the corpus

Logistic damping effect in chemotaxis models with density-suppressed motility (2021, background): “3) in two dimensions were investigated in [5].”
Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities (2022, background): “1) ([9], [1], [8], [28], [2], [3]), as well as some close variants ([12], [6], [11], [14], [30], [37], [22], [23]); beyond this, results on spatially structured large time behavior, and even on the occurrence of infinite-time blow-up ([7], [9], [13], [1], [4]), provide conclusive evidence for signif”
Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities (2022, background): “2) the literature meanwhile provides not only farreaching results on global solvability ([14], [1], [13], [37], [5], [7]; cf.”