Nonlinear stability of phase transition steady states to a hyperbolic–parabolic system modeling vascular networks

DOI10.1112/jlms.12415zbMath1470.35049arXiv2011.07258OpenAlexW3108042383WikidataQ115526863 ScholiaQ115526863MaRDI QIDQ5006334

Hongyun Peng, Changjiang Zhu, Guangyi Hong, Zhi-An Wang

Publication date: 13 August 2021

Published in: Journal of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.07258

zbMATH Keywords

quasilinear hyperbolic-parabolic systemnon-constant phase transition steady statesweighted Hardy-type inequality

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) First-order nonlinear hyperbolic equations (35L60) Cell movement (chemotaxis, etc.) (92C17) Initial-boundary value problems for first-order hyperbolic equations (35L04)

Related Items (5)

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 ⋮ Convergence to nonlinear diffusion waves for a hyperbolic-parabolic chemotaxis system modelling vasculogenesis

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic profile of a parabolic-hyperbolic system with boundary effect arising from tumor angiogenesis
• Stationary solutions with vacuum for a one-dimensional chemotaxis model with nonlinear pressure
• Best asymptotic profile for linear damped \(p\)-system with boundary effect
• Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping
• Global existence and asymptotics of the solutions of the second-order quasilinear hyperbolic equations with the first-order dissipation
• Boundary effect on asymptotic behaviour of solutions to the \(p\)-system with linear damping
• On the stability of homogeneous solutions to some aggregation models
• Optimal convergence rates to diffusion waves for solutions of the hyperbolic conservation laws with damping
• Convergence rates to nonlinear diffusion waves for solutions of system of hyperbolic conservation laws with damping
• Existence and Asymptotic Behavior of Solutions to a Quasi-linear Hyperbolic-Parabolic Model of Vasculogenesis
• Nonlinear Stability of Traveling Waves to a Hyperbolic-Parabolic System Modeling Chemotaxis
• ON A HYPERBOLIC–PARABOLIC SYSTEM MODELING CHEMOTAXIS
• Asymptotic Convergence to Stationary Waves for Unipolar Hydrodynamic Model of Semiconductors
• Existence and Asymptotic Behavior of Solutions to a Semilinear Hyperbolic-Parabolic Model of Chemotaxis
• Global existence of solutions to a hyperbolic-parabolic system
• Boundary spike‐layer solutions of the singular Keller–Segel system: existence and stability
• Phase Transitions and Bump Solutions of the Keller--Segel Model with Volume Exclusion
• Approximation of Hyperbolic Models for Chemosensitive Movement
• A Review of Vasculogenesis Models

This page was built for publication: Nonlinear stability of phase transition steady states to a hyperbolic–parabolic system modeling vascular networks