Stability of rarefaction wave for viscous vasculogenesis model

Abstract

<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M1">\begin{document}$ 2A-\frac{{\mu}a}{b}>0 $\end{document}</tex-math></inline-formula> which guarantees the dissipation of this model.</p>