Existence and asymptotic properties of aerotaxis model with the Fokker–Planck type diffusion. (June 2023)

• Record Type: Journal Article
• Authors: Lee, Jihoon; Yoon, Changwook
• Is Part Of: Nonlinear analysis. Volume 71(2023)
• Publication Date: 2023-06
• Subjects: Global existence -- Keller–Segel -- Chemotaxis -- Aerotaxis -- Fokker–Planck; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103758
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we consider Fokker–Planck type diffusion aerotaxis equations which resemble the usual aerotaxis equations. In view of well-posedness, its own special diffusion structure enables us to take advantage. In two dimensions, we show the existence of global classical solutions under some appropriate conditions. In addition, the stabilization property of the solution is studied, as time approaches infinity. In three dimensions, we prove the existence of global weak solutions.