Global boundedness in a fully parabolic quasilinear chemotaxis system with singular sensitivity
type: Item
instance of: scholarly article
title: Global boundedness in a fully parabolic quasilinear chemotaxis system with singular sensitivity
zbMATH Open document ID: 1429.35038
author: Mengyao Ding
published in: Journal of Mathematical Analysis and Applications
publication date: 2018-03-22T00:00:00Z
review text: In this paper, the author studies the global boundedness of solutions to the quasilinear fully parabolic chemotaxis system: \[ \begin{cases} u_t =\nabla\cdot(D(u)\nabla u -S(u)\nabla \phi(v)), \\ v_t =\Delta v-v+u, \end{cases} \] in a bounded domain \(\Omega\subset\mathbb{R}^n\) (\(n\geq 2\)) subject to the non-flux boundary conditions, the diffusivity fulfills \(D(u) = a_0(u +1)^{-\alpha}\) with \(a_0 > 0\) and \(\alpha\geq 0\), while the density-signal governed sensitivity satisfies \(0\leq S(u)\leq b_0(u +1)^\beta\) and \(0 < \phi'(v) \leq\frac{\chi}{v^k}\) for \(b_0, \chi > 0\) and \(\beta, k\in \mathbb{R}\). It is shown that the solution is globally bounded provided \(\alpha+\beta < 1\) and \(k \leq 1\). This result demonstrates the effect of signal-dependent sensitivity on the blow-up prevention.
reviewed by: Yuanyuan Ke
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35K51
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 92C17
Mathematics Subject Classification ID: 35K59
Mathematics Subject Classification ID: 35Q92
zbMATH DE Number: 6852157
zbMATH Keywords: nonlinear diffusion
zbMATH Keywords: signal-dependent sensitivity
zbMATH Keywords: non-flux boundary conditions
zbMATH Keywords: blow-up prevention
MaRDI profile type: Publication
full work available at URL: j.jmaa.2018.01.049
OpenAlex ID: W2789274442
cites work: Q4254459
cites work: Finite-time blow-up in a quasilinear system of chemotaxis
cites work: Q5630031
cites work: Boundedness in a fully parabolic chemotaxis system with singular sensitivity
cites work: Boundedness in a fully parabolic chemotaxis system with strongly singular sensitivity
cites work: Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with the sensitivity \(v^{-1}S(u)\)
cites work: Boundedness of solutions to parabolic-elliptic Keller-Segel systems with signal-dependent sensitivity
cites work: Boundedness in quasilinear Keller-Segel systems of parabolic-parabolic type on non-convex bounded domains
cites work: On Explosions of Solutions to a System of Partial Differential Equations Modelling Chemotaxis
cites work: Q4354424
cites work: A unified method for boundedness in fully parabolic chemotaxis systems with signal‐dependent sensitivity
cites work: Q4392915
cites work: COMPETING EFFECTS OF ATTRACTION VS. REPULSION IN CHEMOTAXIS
cites work: Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity
cites work: Global boundedness in a quasilinear chemotaxis system with general density-signal governed sensitivity
cites work: Absence of collapse in a parabolic chemotaxis system with signal-dependent sensitivity
cites work: Does a ‘volume-filling effect’ always prevent chemotactic collapse?
cites work: Global solutions in a fully parabolic chemotaxis system with singular sensitivity
cites work: Boundedness and finite-time collapse in a chemotaxis system with volume-filling effect
DOI: 10.1016/J.JMAA.2018.01.049
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description: scientific article; zbMATH DE number 6852157