Asymptotic stability of diffusion waves of a quasi-linear hyperbolic-parabolic model for vasculogenesis

Abstract

In this paper, we derive the large-time profile of solutions to the Cauchy problem of a hyperbolic-parabolic system modeling the vasculogenesis in R 3 . When the initial data are prescribed in the vicinity of a constant ground state, by constructing a time-frequency Lyapunov functional and employing the Fourier energy method and spectral analysis, we show that solution of the Cauchy problem tend time-asymptotically to linear diffusion waves around the constant ground state with algebraic decaying rates under certain conditions on the density-dependent pressure function.

A novel nonlocal partial differential equation model of endothelial progenitor cell cluster formation during the early stages of vasculogenesis

“…Partial di↵erential equation models of single-cell vasculogenesis. Continuum deterministic models in the extant literature can be categorised as Persistence and Endogenous Chemotaxis (PEC) models [3,29,38,58,62,98], modelling the early stages of single-cell vasculogenesis, and mechanochemical models [64,73,74,76], better suited to describe the late stages of the process, with the exception of the work by Tosin et al [111] who proposed a comprehensive model.…”