Existence of bounded global solutions for fully parabolic attraction-repulsion chemotaxis systems with signal-dependent sensitivities and without logistic source
Date
2021-09-10
Authors
Chiyo, Yutaro
Mizukami, Masaaki
Yokota, Tomomi
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
This article concerns the parabolic attraction-repulsion chemo-taxis system with signal-dependent sensitivities
ut = ∆u - ∇ ∙ (uχ(v)∇v) + ∇ ∙ (uξ(w)∇w), x ∈ Ω, t > 0,
vt = ∆v - v + u, x ∈ Ω, t > 0,
wt = ∆w - w + u, x ∈ Ω, t > 0
under homogeneous Neumann boundary conditions and initial conditions, where Ω ⊂ ℝn (n ≥ 2) is a bounded domain with smooth boundary, χ, ξ are functions satisfying certain conditions. Existence of bounded global classical solutions to the system with logistic source and logistic damping have been obtained in [1]. This article establishes the existence of global bounded classical solutions with logistic damping.
Description
Keywords
Chemotaxis, Attraction-repulsion, Existence, Boundedness
Citation
Chiyo, Y., Mizukami, M., & Yokota, T. (2021). Existence of bounded global solutions for fully parabolic attraction-repulsion chemotaxis systems with signal-dependent sensitivities and without logistic source. <i>Electronic Journal of Differential Equations, 2021</i>(71), pp. 1-10.
Rights
Attribution 4.0 International