Classical solutions to a logistic chemotaxis model with singular sensitivity and signal absorption. (April 2019)

• Record Type: Journal Article
• Authors: Lankeit, Elisa; Lankeit, Johannes
• Is Part Of: Nonlinear analysis. Volume 46(2019)
• Page Start: 421
• Page End: 445
• Publication Date: 2019-04
• Subjects: Chemotaxis -- Classical solution -- Singular sensitivity -- Signal consumption -- Global existence -- Boundedness -- Logistic source; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.09.012
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: Assuming that 0 < χ < 2 n, κ ≥ 0 and μ > n − 2 2 n, we prove global existence of classical solutions to a chemotaxis system slightly generalizing u t = Δ u − χ ∇ ⋅ ( u v ∇ v ) + κ u − μ u 2 v t = Δ v − u v in a bounded domain Ω ⊂ R n, with homogeneous Neumann boundary conditions and for widely arbitrary positive initial data. In the spatially one-dimensional setting, we prove global existence and, moreover, boundedness of the solution for any χ > 0, μ > 0, κ ≥ 0 .