Convergence to nonlinear diffusion waves for a hyperbolic-parabolic chemotaxis system modelling vasculogenesis

2021/11/17 by Qingqing Liu, Liu, Qingqing, Hongyun Peng +3 · 1 citation
Computer Science · Mathematics · Medicine · #35A01 #35B40 #35B45 #35K57 #35Q92 #92C17 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #MRI in cancer diagnosis #Mathematical Biology Tumor Growth

paper · pdf · doi:10.48550/arxiv.2111.09165

openalex publication_date 2021/11/17 · openalex created_date 2021/11/22 · openalex updated_date 2026/07/28

Abstract

In this paper, we are concerned with a quasi-linear hyperbolic-parabolic system of persistence and endogenous chemotaxis modelling vasculogenesis in ℝ. Under some suitable structural assumption on the pressure function, we first predict the system admits a nonlinear diffusion wave in ℝ based on the empirical results in the literature. Then we show that the solution of the concerned system will locally and asymptotically converges to this nonlinear diffusion wave if the wave strength is small. By using the time-weighted energy estimates, we further prove that the convergence rate of the nonlinear diffusion wave is algebraic.

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