Boundedness enforced by mildly saturated conversion in a chemotaxis-May–Nowak model for virus infection
- verfasst von
- Mario Fuest
- Abstract
We study the system (⋆){u
t=Δu−∇⋅(u∇v)−u−f(u)w+κ,v
t=Δv−v+f(u)w,w
t=Δw−w+v, which models the virus dynamics in an early stage of an HIV infection, in a smooth, bounded domain Ω⊂R
n,n∈N, for a parameter κ≥0 and a given function f∈C
1([0,∞)) satisfying f≥0, f(0)=0 and f(s)≤K
fs
α for all s≥1, some K
f>0 and α∈R. We prove that whenever α<[Formula presented], solutions to (⋆) exist globally and are bounded. The proof mainly relies on smoothing estimates for the Neumann heat semigroup and (in the case α>1) on a functional inequality. Furthermore, we provide some indication why the exponent [Formula presented] could be essentially optimal.
- Externe Organisation(en)
-
Universität Paderborn
- Typ
- Artikel
- Journal
- Journal of Mathematical Analysis and Applications
- Band
- 472
- Seiten
- 1729-1740
- Anzahl der Seiten
- 12
- ISSN
- 0022-247X
- Publikationsdatum
- 04.2019
- Publikationsstatus
- Veröffentlicht
- Peer-reviewed
- Ja
- ASJC Scopus Sachgebiete
- Analysis, Angewandte Mathematik
- Ziele für nachhaltige Entwicklung
- SDG 3 – Gute Gesundheit und Wohlergehen
- Elektronische Version(en)
-
https://doi.org/10.1016/j.jmaa.2018.12.020 (Zugang:
Offen)
