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<p>In this paper, we study the global existence for a quasi-linear hyperbolic-parabolic system modeling vascular networks. Under the assumption that the critical cell density satisfies <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="21_2025_974_Article_IEq1.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="88" /> </InlineMediaObject> <EquationSource Format="TEX">\(P'(\bar{\rho })=\frac{a\mu }{b}\bar{\rho }\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>P</mi> <mo>′</mo> </msup> <mrow> <mo stretchy="false">(</mo> <mover accent="true"> <mrow> <mi>ρ</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>a</mi> <mi>μ</mi> </mrow> <mi>b</mi> </mfrac> <mover accent="true"> <mrow> <mi>ρ</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> </mrow> </math></EquationSource> </InlineEquation>, we establish the global existence for small perturbations and derive the optimal convergent rates for all-order derivatives of the solution.</p>

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Global Existence of a Quasi-Linear Hyperbolic-Parabolic Model for Vasculogenesis

  • 期刊论文

  • 发表日期：

    2025年10月3日

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  • Qing Chen,
  • Yunshun Wu

摘要

In this paper, we study the global existence for a quasi-linear hyperbolic-parabolic system modeling vascular networks. Under the assumption that the critical cell density satisfies \(P'(\bar{\rho })=\frac{a\mu }{b}\bar{\rho }\) P ′ ( ρ ¯ ) = a μ b ρ ¯ , we establish the global existence for small perturbations and derive the optimal convergent rates for all-order derivatives of the solution.