An n-dimensional chemotaxis system with signal-dependent motility and generalized logistic source: global existence and asymptotic stabilization

By Wenbin Lv, Qingyuan Wang. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2020

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Abstract This paper deals with the global existence for a class of Keller–Segel model with signal-dependent motility and general logistic term under homogeneous Neumann boundary conditions in a higher-dimensional smoothly bounded domain, which can be written as $$\eqalign{& u_t = \Delta (\gamma (v)u) + \rho u-\mu u^l,\quad x\in \Omega ,\;t > 0, \cr & v_t = \Delta v-v + u,\quad x\in \Omega ,\;t > 0.} $$It is shown that whenever ρ ∈ ℝ, μ > 0 and $$l > \max \left\{ {\displaystyle{{n + 2} \over 2},2} \right\},$$then the considered system possesses a global classical solution for all sufficiently smooth initial data. Furthermore, the solution converges to the equilibrium $$\left( {{\left( {\displaystyle{{\rho _ + } \over \mu }} \right)}^{1/(l-1)},{\left( {\displaystyle{{\rho _ + } \over \mu }} \right)}^{1/(l-1)}} \right)$$as t → ∞ under some extra hypotheses, where ρ+ = max{ρ, 0}.

Subfields: Genetics, Modeling and Simulation, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/8f1e3f8fa10de3c2d4d43d751a0901a80e3c9513

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Citations in the corpus

Logistic damping effect in chemotaxis models with density-suppressed motility (2021, background): “In [25, 26], the global boundedness of solutions to the parabolic-parabolic version of (1.”
A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion (2022, background): “2) or certain closely related variants stabilize toward homogeneous equilibria ([13], [34], [8], [15], [26], [28], [29], [27], [42]).”
Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities (2022, background): “also [19], [21], [38], [45], [28], [29] and [30] for corresponding studies on some close relatives), but also on large time asymptotics, and especially on the identification of situations in which either stabilization toward equilibria can be observed, or, alternatively, infinite-time blow-up occurs”