@article{Lv2026, 
author = {Wenjuan Lv},
title = {Global existence and boundedness of HIV chemotaxis model with nonlinear diffusions},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {4},
pages = {10257-10273},
keywords = {HIV model, immune chemokines, nonlinear diffusion, global existence},
url = {https://www.sciopen.com/article/10.3934/math.2026424},
doi = {10.3934/math.2026424},
abstract = {This paper investigates a class of reaction-diffusion models that describing the chemotactic movement of cytotoxic T lymphocytes (CTLs) in HIV-1 infection, thereby incorporating nonlinear diffusion mechanisms for CD       4          +      T cells, infected cells, and CTLs. Assuming that the CTL diffusion coefficient satisfies        D    3    (  w  )  ≥            D      ^        (  w  +  1      )    θ   with    θ  >  1, and the chemotactic sensitivity function satisfies        |    χ  (  w  )      |    ≤            χ      ^        w  (  1  +  w      )          η      −      1       with    η  ≤  1, this study proves, via energy estimates, semigroup techniques, and the Moser iteration, provided    θ  >  1 and    η  ≤  1, that the classical solutions globally-exist and are unique and uniformly bounded for any spatial dimension    n  ≥  1. The results demonstrate that a sufficiently strong nonlinear diffusion (with    θ  >  1) can effectively suppress chemotaxis-driven instability, thus ensuring the boundedness of the systems long-term behavior. This research provides mathematical theoretical support to understand the regulatory role of immune chemotactic movement in viral dynamics.}
}