Application of the best constant of the Sobolev inequality to degenerate Keller-Segel models

By Yoshie Sugiyama. Advances in Differential Equations, 2007

58 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/48549fb9faf4872fc6652fc9c47769f71e0d6d19

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Citations in the corpus

Equilibria of homogeneous functionals in the fair-competition regime (2016, background): “The role of both non-linear diffusion and non-local aggregation terms was clarified in [7], see also [50], where the authors find that there is a similar dichotomy to the two-dimensional classical Keller–Segel case (N = 2,m = 1, k = 0), for a whole range of parameters, choosing the non-local term as”
Existence, Uniqueness and Lipschitz Dependence for Patlak–Keller–Segel and Navier–Stokes in $${\mathbb{R}^2}$$R2 with Measure-Valued Initial Data (2012, background): “1) involving nonlinear diffusion which are critical in higher dimensions have also been studied [51, 14, 65, 66, 10, 50] (see also the related [53]).”
On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher (2011, background): “(32) This difference of balance was studied to obtain Theorem 13 (First criticality, [54, 55]).”
Local and global well-posedness for aggregation equations and Patlak–Keller–Segel models with degenerate diffusion (2010, methodology): “Moreover, in the case of the Newtonian or Bessel potential, m = 2 − 2/d and the critical diffusion exponent of the PKS models discussed in [13, 57, 58] is recovered.”
Existence, Uniqueness and Lipschitz Dependence for Patlak-Keller-Segel and Navier-Stokes in R2 with Measure-valued Initial Data (2012, background): “1) involving nonlinear diffusion which are critical in higher dimensions have also been studied [10,14,50,51,65,66] (see also the related [53]).”
Critical mass for a Patlak–Keller–Segel model with degenerate diffusion in higher dimensions (2008, methodology): “2 Existence criterion As in [30, 31], we consider the regularised problem”