Free Energy and Self-Interacting Particles

By Takashi Suzuki. 2005

203 citations recorded by the source corpus.

Subfields: Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5c58579f31b77475ab30f80ea4356d32201a6204

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In Statistical and Nonlinear Physics

Citations in the corpus

Infinite time aggregation for the critical Patlak‐Keller‐Segel model in ℝ2 (2007, result): “We also refer to [50, 53] and references therein.”
Blowup Solutions of Some Nonlinear Elliptic Equations Involving Exponential Nonlinearities (2006, background): “In Suzuki’s book [15], this fact is summarized as the quantized blowup mechanism in the non-equilibrium mean field of self-gravitating particles and in the system of chemotaxis.”
Competing effects of attraction vs. repulsion in chemotaxis (2013, background): “A well-known chemotaxis model was initially proposed by Keller and Segel(27) and has been extensively studied in the past four decades from various perspectives.(19,22,44,18,25,26,51,53) Among the theoretical results, the blow-up of solutions in finite time is a striking indication of the spontaneou”
Conservative upwind finite-element method for a simplified Keller–Segel system modelling chemotaxis (2007, methodology): “For further details and other methods of time discretization, we refer to Saito & Suzuki (2005).”
Global existence for chemotaxis with finite sampling radius (2006, background): “…global existence depends on a threshold: when the initial mass lies below the threshold solutions exist globally , while above the threshold solutions blow up in finite time (see references in Horstmann [12], or the new book of Suzuki [32], and Dolbeault and Perthame [7] for a recent result).”
A Chemotaxis System with Logistic Source (2007, background): “also Jager and Luckhaus, 1992 for a closely related problem and Horstmann, 2003 or Suzuki, 2005 for a survey).”
An n-dimensional chemotaxis system with signal-dependent motility and generalized logistic source: global existence and asymptotic stabilization (2020, background): “15 T. Suzuki 2005 Free energy and self-interacting particles.”
Nondegeneracy of blow-up points for the parabolic Keller–Segel system (2014, background): “When N = 2, it is known (see [47] and the references therein) that blow-up points are isolated and that, near each blow-up point x0, u(t, ·) converges to a multiple Kδx0 of the Dirac mass as t → T , with K = 8π if x0 ∈ Ω and K = 4π if x0 ∈ ∂Ω .”
A user’s guide to PDE models for chemotaxis (2009, background): “Detailed reviews can be found in the survey of Horstmann [40], and in the textbooks of Suzuki [98] and Perthame [87].”
A quasi-linear parabolic system of chemotaxis (2006, unknown): “� u0� 1 c ∗ ([8,11,12,17]).This phenomenon was conjectured by [4] and gave a motivation of our previous works on the mass quantization of collapses in the blowup solution. See [19, 20 ] for more details.”
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.”