Existence and Asymptotic Behavior of Solutions to a Quasi-linear Hyperbolic-Parabolic Model of Vasculogenesis

DOI10.1137/110858896zbMath1282.35060arXiv1112.1940OpenAlexW1991781074MaRDI QIDQ2840371

Alice Sepe, C. Di Russo

Publication date: 18 July 2013

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.1940

zbMATH Keywords

dissipativityGreen functionKawashima-Shizuta's conditions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) First-order nonlinear hyperbolic equations (35L60) Developmental biology, pattern formation (92C15) Initial value problems for first-order hyperbolic systems (35L45) Euler equations (35Q31)

Related Items (9)

Asymptotic Stability of Diffusion Waves of a Quasi-Linear Hyperbolic-Parabolic Model for Vasculogenesis ⋮ The Hyperbolic-Parabolic Chemotaxis System for Vasculogenesis: Global Dynamics and Relaxation Limit Toward a Keller–Segel Model ⋮ Convergence to nonlinear diffusion waves for solutions of hyperbolic-parabolic chemotaxis system ⋮ Large time behavior of a hyperbolic-parabolic model of vasculogenesis ⋮ A survey on well-balanced and asymptotic preserving schemes for hyperbolic models for chemotaxis ⋮ Convergence to nonlinear diffusion waves for a hyperbolic-parabolic chemotaxis system modelling vasculogenesis ⋮ Stability of rarefaction wave for viscous vasculogenesis model ⋮ Nonlinear stability of phase transition steady states to a hyperbolic–parabolic system modeling vascular networks ⋮ A numerical comparison between degenerate parabolic and quasilinear hyperbolic models of cell movements under chemotaxis

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