Open AccessStability of rarefaction wave for viscous vasculogenesis model
Author(s) -
Qingqing Liu,
Xiaoli Wu
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2022034
Subject(s) - vasculogenesis , perturbation (astronomy) , rarefaction (ecology) , mathematics , dissipation , cauchy distribution , physics , mathematical analysis , mathematical physics , thermodynamics , quantum mechanics , geology , chemistry , paleontology , biochemistry , species richness , endothelial stem cell , in vitro
In this paper, we are concerned with the large time behavior of solutions to the one-dimensional Cauchy problem on a hyperbolic-parabolic-elliptic model for vasculogenesis in the case when far field states of initial data are distinct. It turns out that the solutions exist for all time and tend to a weak rarefaction wave whose strength is not necessarily small under small perturbation. All the results are based on the assumption \begin{document}$ 2A-\frac{{\mu}a}{b}>0 $\end{document} which guarantees the dissipation of this model.