Boundedness of Classical Solutions to a Degenerate Keller–Segel Type Model with Signal-Dependent Motilities

By Kentarou Fujie, Jie Jiang. Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications, 2020

75 citations recorded by the source corpus.

In this paper, we consider the initial Neumann boundary value problem for a degenerate kinetic model of Keller–Segel type. The system features a signal-dependent decreasing motility function that vanishes asymptotically, i.e., degeneracies may take place as the concentration of signals tends to infinity. In the present work, we are interested in the boundedness of classical solutions when the motility function satisfies certain decay rate assumptions. Roughly speaking, in the two-dimensional setting, we prove that classical solution is globally bounded if the motility function decreases slower than an exponential speed at high signal concentrations. In higher dimensions, boundedness is obtained when the motility decreases at certain algebraical speed. The proof is based on the comparison methods developed in our previous work (Fujie and Jiang in J. Differ. Equ. 269:5338–5778, 2020; Fujie and Jiang in Calc. Var. Partial Differ. Equ. 60:92, 2021) together with a modified Alikakos–Moser type iteration. Besides, new estimations involving certain weighted energies are also constructed to establish the boundedness.

Subfields: Cell Biology, Modeling and Simulation, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/2eb50c103de1c241a2af58d431e4aedb1998cd44

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Cell Biology

In Modeling and Simulation

In Molecular Biology

Citations in the corpus

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”
Logistic damping effect in chemotaxis models with density-suppressed motility (2021, background): “Meanwhile, it was proved in [8, 39, 41] that global bounded classical solutions exist in all dimensions with some”
A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion (2022, unknown): “Besides basic results on global solvability (see [1], [14], [11], [10], [4], [15], [35], [34] and also [40]), several studies also include findings on asymptotic behavior, mainly identifying diffusion-dominated constellations in which solutions to either (1.”
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.”
Global existence and infinite time blow-up of classical solutions to chemotaxis systems of local sensing in higher dimensions (2021, unknown): “1) with some polynomial decaying function γ are obtained under smallness conditions on some parameters in [18, 3, 6].”