ASYMPTOTIC STABILITY OF DIFFUSION WAVES OF A QUASI-LINEAR HYPERBOLIC-PARABOLIC MODEL FOR VASCULOGENESIS

Qingqing Liu, Hongyun Peng, Zhi An Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

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.

Original languageEnglish
Pages (from-to)1313-1346
Number of pages34
JournalSIAM Journal on Mathematical Analysis
Volume54
Issue number1
DOIs
Publication statusE-pub ahead of print - 24 Feb 2022

Keywords

  • Darcy's law
  • diffusion waves
  • hyperbolic-parabolic model
  • spectral analysis
  • vasculogenesis

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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