Global boundedness and finite time blow-up of solutions for a quasilinear chemotaxis-May-Nowak model

2025/03/31 by Wang, Jianping, Wang, Mingxin
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.23645

Abstract

In this paper, we introduce the nonlinear diffusion term ∇⋅(D(u)∇ u) into the chemotaxis-May-Nowak model to investigate the effects of D(u) and chemotaxis on the global existence, boundedness, and finite time blow-up of solutions. Here, D(u) generalizes the prototype (1+u)^m-1 with m∈\R. For the parabolic-elliptic-parabolic case, if m>2+(n)/(2)-\frac2n when n≥3 and m>\frac32 when n=2, then all solutions exist globally and remain bounded, whereas if n∈\2,3\ and m<1, finite time blow-up occurs when Ω is a ball and the initial data are radially symmetric. For the fully parabolic case, if m>1+(n)/(2)-\frac2n, then all solutions exist globally and remain bounded.

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