Boundedness enforced by mildly saturated conversion in a chemotaxis-May–Nowak model for virus infection
- authored by
- 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.
- External Organisation(s)
-
Paderborn University
- Type
- Article
- Journal
- Journal of Mathematical Analysis and Applications
- Volume
- 472
- Pages
- 1729-1740
- No. of pages
- 12
- ISSN
- 0022-247X
- Publication date
- 04.2019
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- Analysis, Applied Mathematics
- Sustainable Development Goals
- SDG 3 - Good Health and Well-being
- Electronic version(s)
-
https://doi.org/10.1016/j.jmaa.2018.12.020 (Access:
Open)
