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http://hdl.handle.net/10397/95652
Title: | Asymptotic stability of diffusion waves of a quasi-linear hyperbolic-parabolic model for vasculogenesis | Authors: | Liu, Q Peng, H Wang, ZA |
Issue Date: | 2022 | Source: | SIAM journal on mathematical analysis, 2022, v. 54, no. 1, p. 1313-1346 | 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 |
Publisher: | Society for Industrial and Applied Mathematics | Journal: | SIAM journal on mathematical analysis | ISSN: | 0036-1410 | EISSN: | 1095-7154 | DOI: | 10.1137/21M1418150 | Rights: | © 2022 Society for Industrial and Applied Mathematics The following publication Gui, X., Li, B., & Wang, J. (2022). Convergence of Renormalized Finite Element Methods for Heat Flow of Harmonic Maps. SIAM Journal on Numerical Analysis, 60(1), 312-338 is available at https://doi.org/10.1137/21M1402212. |
Appears in Collections: | Journal/Magazine Article |
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