On a quasilinear parabolic–elliptic chemotaxis system with logistic source

By Liangchen Wang, Chunlai Mu, Pan Zheng. 2014

185 citations recorded by the source corpus.

Subfields: Cell Biology, Computational Theory and Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/48c5adcd75092bcf7c87b5892e3115087607a263

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 Computational Theory and Mathematics

In Modeling and Simulation

Citations in the corpus

An attraction‐repulsion chemotaxis system with logistic source (2016, background): “[21] obtained the boundedness of solutions to the nonlinear-diffusion model with such proliferation term.”
Global existence and asymptotic behavior of classical solutions to a parabolic-elliptic chemotaxis system with logistic source on $\mathbb{R}^{N}$ (2016, background): “The reader is referred to [2], [7], [14], [40], [43], [45], [46], [47], [49], [50], [52], and references therein for other studies of (1.”
Finite-time blow-up in low-dimensional Keller–Segel systems with logistic-type superlinear degradation (2018, background): “1), inter alia accounting for nonlinear cell diffusion ([51], [6], [41], [55], [58]), for variants in the cross-diffusive interaction ([53], [20], [4], [39], [57]) or also in the signal evolution, or even containing couplings to further mechanisms and components such as haptotactic cues ([5], [40], ”
Global existence of solutions and uniform persistence of a diffusive predator-prey model with prey-taxis ✩ (2016, background): “Global existence, boundedness or blowup of solutions in more general quasilinear parabolic– parabolic chemotaxis systems with nonlinear sensitivity functions and source term have been studied extensively, see for example, [11,12,25,26,34,44,48,49,59,61,62].”
How strong a logistic damping can prevent blow-up for the minimal Keller–Segel chemotaxis system? (2016, background): “1) have been considered to provide conditions on diffusion, degradation, chemo-sensitivity and mostly on the growth source ensuring the boundedness of the proposed models [1, 5, 29, 36, 43, 48, 49, 61, 64, 65] and the references therein, and that explosion of solutions is possible in chemotaxis syst”
Boundedness and global existence in the higher-dimensional parabolic–parabolic chemotaxis system with/without growth source (2015, background): “Then a lot of variants of parabolic–elliptic simplifications have been considered, see [48,14, 53,11,46] and the references therein.”
Dynamics in a parabolic-elliptic chemotaxis system with growth source and nonlinear secretion (2019, background): “[3, 5, 9, 22, 30], for a system with nonlinear diffusion, nonlinear chemosensitivity, generalized logistic source or nonlinear production.”