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

2021/03/21 by Liu, Qinging, Peng, Hongyun, Wang, Zhi-An · 1 citation
#35B40 #35L04 #35L60 #35Q92 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2103.11301

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 \R³. 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.

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