Global existence and decay properties for a degenerate Keller–Segel model with a power factor in drift term

By Yoshie Sugiyama, Hiroko Kunii. 2006

202 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Molecular Biology, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/1b5efd1d3393c733140e2ef2f09774fbfe690157

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Citations in the corpus

Global existence and asymptotic behavior of classical solutions to a parabolic-elliptic chemotaxis system with logistic source on $\mathbb{R}^{N}$ (2016, unknown): “2) when Ω is the whole space R and f(u, v) = 0 (see [8],[17] [28], [36], [35]).”
Finite-time blow-up in a quasilinear system of chemotaxis (2008, background): “When n = 1 the authors of [18, 19, 21] have much more restrictive assumptions on the nonlinearity φ than needed.”
Local existence and finite time blow-up of solutions in the 2-D Keller-Segel system (2008, background): “(seee.g. Yagi [22], Diaz-Nagai-Rakotoson [4] and Sugiyama-Kunii [ 20 ].) Our construction requires only L 1 -property of u0. If in addition u0 ∈ L 1 ∩ L q∗ (R 2 ) for some q∗ > 1, then we can characterize the time interval of its local existence by means of the L q∗ -norm of”
Global strong solution to the semi-linear Keller-Segel system of parabolic-parabolic type with small data in scale invariant spaces (2009, unknown): “Moreover, in [26,27], the following decay rate was obtained ∥∥u(t)∥∥p + ∥∥v(t)∥∥p = O (t− n n(m−1)+2 (1− (1)p )), 1 p ∞, as t → ∞.”
Equilibria of homogeneous functionals in the fair-competition regime (2016, background): “For the Newtonian case, global existence vs blow-up of weak solutions has been investigated for the diffusion coefficients m = 1 [30], 1 < m ≤ 2− 2 N [49,52], m = 2N N+2 [26], 2N N+2 < m < 2− 2 N [27,39] and for the whole range 0 < m ≤ 2 − 2 N [4].”
Nondegeneracy of blow-up points for the parabolic Keller–Segel system (2014, background): “When the chemosensitivity function φ(s) behaves for large s like s with m > 2/N , blow-up in finite time occurs independently of the magnitude of initial mass provided the data are concentrated enough, whereas all solutions exist globally if m < 2/N (see [12,29,35,45]).”