@article{99741014b3cc41d09b230563479bd193,
title = "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 delicate spectral analysis, we show that solutions of the Cauchy problem tend time-asymptotically to linear diffusion waves around the constant ground state with algebraic decaying rates under suitable conditions on the density-dependent pressure function.",
keywords = "Darcy's law, diffusion waves, hyperbolic-parabolic model, spectral analysis, vasculogenesis",
author = "Qingqing Liu and Hongyun Peng and Wang, \{Zhi An\}",
note = "Funding Information: \textbackslash{}ast Received by the editors May 6, 2021; accepted for publication (in revised form) November 5, 2021; published electronically February 24, 2022. https://doi.org/10.1137/21M1418150 Funding: The work of the first author was supported by National Natural Science Foundation of China grant 12071153, Guangdong Basic and Applied Basic Research Foundation grants 2021A1515012360, Guangzhou Science and Technology Program 202102021137, and Fundamental Research Funds for the Central Universities grant 2020ZYGXZR032. The work of the second author was supported by National Natural Science Foundation of China grant 11901115, Natural Science Foundation of Guangdong Province grant 2019A1515010706, and GDUT grant 220413228. The work of the third author was partially supported by Hong Kong Research Grant Council General Research Fund grant PolyU 15304720, project P0032967. Publisher Copyright: {\textcopyright} 2022 Society for Industrial and Applied Mathematics.",
year = "2022",
month = feb,
day = "24",
doi = "10.1137/21M1418150",
language = "English",
volume = "54",
pages = "1313--1346",
journal = "SIAM Journal on Mathematical Analysis",
issn = "0036-1410",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "1",
}