A logarithmic chemotaxis model featuring global existence and aggregation. (December 2019)

• Record Type: Journal Article
• Authors: Desvillettes, Laurent; Kim, Yong-Jung; Trescases, Ariane; Yoon, Changwook
• Is Part Of: Nonlinear analysis. Volume 50(2019)
• Page Start: 562
• Page End: 582
• Publication Date: 2019-12
• Subjects: Asymmetric diffusion -- Keller–Segel equations -- Duality lemma -- Cross-diffusion -- Cell-aggregation -- Pattern formation; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.05.010
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: The global existence of a chemotaxis model for cell aggregation phenomenon is obtained. The model system belongs to the class of logarithmic models and takes a Fokker–Planck type diffusion for the equation of cell density. We show that weak solutions exist globally in time in dimensions n ∈ { 1, 2, 3 } and for large initial data. The proof covers the parameter regimes that constant steady states are linearly stable. It also partially covers the other parameter regimes that constant steady states are unstable. We also find the sharp instability condition of constant steady states and provide numerical simulations which illustrate the formation of aggregation patterns.