Blowup of nonradial solutions to parabolic–elliptic systems modeling chemotaxis in two-dimensional domains

By T. Nagai. 2001

457 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/3324c399a5fb364fe7eaee105bbc1d3d104bf928

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Citations in the corpus

Critical mass for infinite-time aggregation in a chemotaxis model with indirect signal production (2016, background): “For parabolic-elliptic Keller-Segel systems, rigorous proofs for this can be found in, or easily adapted from [26] and [25]; in the parabolic-parabolic case, only a respective boundedness result is available in the case ∫ Ω u0 < 4π ([25]), whereas the occurrence of any nonradial finite-time blow-up ”
Finite-time blow-up in low-dimensional Keller–Segel systems with logistic-type superlinear degradation (2018, background): “Indeed, while phenomena of blow-up in finite time constitute one of the certainly most characteristic effects of chemotactic cross-diffusion in frameworks of pure Keller-Segel systems without cell kinetics ([13], [25], [11], [45]), for the more complex system (1.”
Combining effects ensuring boundedness in an attraction–repulsion chemotaxis model with production and consumption (2022, background): “These results are included in more general analyses, dealing with the existence and properties (globality, uniform boundedness, or blow-up) of solutions to the Cauchy problem associated to (1), specially for the parabolic-elliptic version corresponding to the choice τ = 0; for details we mention [10”
Finite-time blowup and global-in-time unbounded solutions to a parabolic–parabolic quasilinear Keller–Segel system in higher dimensions (2011, background): “1) in both radially symmetric ond non-radial settings (see [13], [14], [15]).”
The drift–diffusion system in two-dimensional critical Hardy space (2008, unknown): “[1,28,29,41–44,46,47,51–53,56]).”
Nondegeneracy of blow-up points for the parabolic Keller–Segel system (2014, background): “In the nonradial bounded domain case, the threshold phenomenon was also established, and it was shown that the critical mass is actually 4π instead of 8π , due to the possibility of boundary blow-up points (see [3,36,38]).”
Blow-up in a higher-dimensional chemotaxis system despite logistic growth restriction (2011, background): “1) is replaced with the parabolic equation vt = ∆v − v + u ([15], [1], [16], [10], [7], cf.”
Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics (2016, unknown): “Without kinetic terms, that is, when μ1 = μ2 = 0, the resulting system then inherits some important properties from the original Keller-Segel model for single-species chemotaxis; in particular, the striking phenomenon of finite-time blow-up, known to occur in both parabolic-elliptic and fully parabo”
Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities (2022, result): “These observations are quite in line with numerous findings on emergence and stabilization of singular structures ([17], [31], [34], [33], [4], [6]), and supplementary also of more subtle destabilization of spatial homogeneity ([40]), in various further among the chemotaxisproduction versions of (1.”