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

Qinging Liu; Hongyun Peng; Zhi-An Wang

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arXiv · 2103.11301

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

Qinging Liu·Hongyun Peng·Zhi-An Wang

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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.

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Qinging Liu, Hongyun Peng, Zhi-An Wang. 2021-03-21. Asymptotic stability of diffusion waves of a quasi-linear hyperbolic-parabolic model for vasculogenesis. https://arxiv.org/abs/2103.11301

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