Journal
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Volume 54, Issue 1, Pages 1313-1346Publisher
SIAM PUBLICATIONS
DOI: 10.1137/21M1418150
Keywords
hyperbolic-parabolic model; vasculogenesis; Darcy's law; diffusion waves; spectral analysis
Categories
Funding
- National Natural Science Foundation of China [11901115]
- Guangdong Basic and Applied Basic Research Foundation [2021A1515012360]
- Guangzhou Science and Technology Program [202102021137]
- Fundamental Research Funds for the Central Universities grant [2020ZYGXZR032]
- Natural Science Foundation of Guangdong Province [2019A1515010706]
- GDUT [220413228]
- Hong Kong Research Grant Council General Research Fund [PolyU 15304720, P0032967]
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This paper derives the large-time profile of solutions to the Cauchy problem of a hyperbolic-parabolic system modeling the vasculogenesis in R-3. By constructing a time-frequency Lyapunov functional and employing the Fourier energy method and delicate spectral analysis, the paper shows 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.
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.
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