2021/11/17 by Qingqing Liu, Liu, Qingqing, Hongyun Peng +4 · 2 citations
Computer Science · Mathematics · Medicine · #35A01 #35B40 #35B45 #35K57 #35Q92 #92C17 #Advanced Mathematical Modeling in Engineering #Algebraic number #Analysis of PDEs (math.AP) #Applied mathematics #Computer science #Convergence (economics) #Diffusion #Economics #FOS: Mathematics #Function (biology) #Hyperbolic function #MRI in cancer diagnosis #Mathematical Biology Tumor Growth #Mathematical analysis #Mathematics #Nonlinear system #Physics #Rate of convergence #Telecommunications #math.AP #msc:35A01 #msc:35B40 #msc:35B45 #msc:35K57 #msc:35Q92 #msc:92C17
paper · pdf · doi:10.48550/arxiv.2111.09165
published in arXiv (Cornell University) (Cornell University)
arxiv created 2021/11/17 · openalex publication_date 2021/11/17 · arxiv updated 2021/11/18 · openalex created_date 2021/11/22 · openalex updated_date 2026/08/05
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.