Global existence and boundedness of HIV chemotaxis model with nonlinear diffusions

Wenjuan Lv; Wenjuan Lv

doi:10.3934/math.2026424

AIMS Mathematics

2026, Volume 11, Issue 4: 10257-10273. doi: 10.3934/math.2026424

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Research article

Global existence and boundedness of HIV chemotaxis model with nonlinear diffusions

Wenjuan Lv ^,

School of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received: 09 March 2026 Revised: 01 April 2026 Accepted: 07 April 2026 Published: 15 April 2026
MSC : 35A01

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) \geq \hat{D}(w+1)^\theta $ with $ \theta > 1 $, and the chemotactic sensitivity function satisfies $ |\chi(w)| \leq \hat{\chi} w(1+w)^{\eta-1} $ with $ \eta \leq 1 $, this study proves, via energy estimates, semigroup techniques, and the Moser iteration, provided $ \theta > 1 $ and $ \eta\leq1 $, that the classical solutions globally-exist and are unique and uniformly bounded for any spatial dimension $ n\geq 1 $. The results demonstrate that a sufficiently strong nonlinear diffusion (with $ \theta > 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.
- HIV model,
- immune chemokines,
- nonlinear diffusion,
- global existence
Citation: Wenjuan Lv. Global existence and boundedness of HIV chemotaxis model with nonlinear diffusions[J]. AIMS Mathematics, 2026, 11(4): 10257-10273. doi: 10.3934/math.2026424

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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) \geq \hat{D}(w+1)^\theta $ with $ \theta > 1 $, and the chemotactic sensitivity function satisfies $ |\chi(w)| \leq \hat{\chi} w(1+w)^{\eta-1} $ with $ \eta \leq 1 $, this study proves, via energy estimates, semigroup techniques, and the Moser iteration, provided $ \theta > 1 $ and $ \eta\leq1 $, that the classical solutions globally-exist and are unique and uniformly bounded for any spatial dimension $ n\geq 1 $. The results demonstrate that a sufficiently strong nonlinear diffusion (with $ \theta > 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.

References

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