Stability of Boundary Layers for a Viscous Hyperbolic System Arising from Chemotaxis: One-Dimensional Case

DOI10.1137/17M112748XzbMath1394.35025OpenAlexW2808154787WikidataQ129700664 ScholiaQ129700664MaRDI QIDQ4566418

Zhi-An Wang, Cheng-Jie Liu, Qianqian Hou, Ya-Guang Wang

Publication date: 15 June 2018

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

Full work available at URL: https://doi.org/10.1137/17m112748x

zbMATH Keywords

energy estimatesCole-Hopf transformationasymptotic analysislogarithmic singularityouter layer solutioninner layer solution

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Cell movement (chemotaxis, etc.) (92C17) Blow-up in context of PDEs (35B44)

Related Items

Global solvability to a singular chemotaxis-consumption model with fast and slow diffusion and logistic source ⋮ Riemann problem for a non-strictly hyperbolic system in chemotaxis ⋮ Global solutions to the free boundary value problem of a chemotaxis-Navier–Stokes system ⋮ Asymptotic behavior of solutions to a chemotaxis-logistic model with transitional end-states ⋮ Construction of unique mild solution and continuity of solution for the small initial data to 1-D Keller-Segel system ⋮ Boundary layer problem on the chemotaxis model with Robin boundary conditions ⋮ Convergence rate of solutions towards spiky steady state for the Keller-Segel system with logarithmic sensitivity ⋮ Vanishing Shear Viscosity Limit for the Navier–Stokes Equations with Cylindrical Symmetry: Boundary Layer and Optimal Convergence Rate ⋮ BV solutions to a hyperbolic system of balance laws with logistic growth ⋮ Acceleration of propagation in a chemotaxis‐growth system with slowly decaying initial data ⋮ Nonlinear stability of strong traveling waves for a chemotaxis model with logarithmic sensitivity and periodic perturbations ⋮ Traveling wave solutions of a singular Keller-Segel system with logistic source ⋮ Controlled dynamics of a chemotaxis model with logarithmic sensitivity by physical boundary conditions ⋮ Boundary-layer profile of a singularly perturbed nonlocal semi-linear problem arising in chemotaxis ⋮ Optimal convergence rate of the vanishing shear viscosity limit for compressible Navier-Stokes equations with cylindrical symmetry ⋮ Asymptotic dynamics of a system of conservation laws from chemotaxis ⋮ Asymptotic stability of exogenous chemotaxis systems with physical boundary conditions ⋮ Nonlinear stability of strong traveling waves for the singular Keller-Segel system with large perturbations ⋮ Convergence of boundary layers for the Keller-Segel system with singular sensitivity in the half-plane ⋮ Global dynamics and zero-diffusion limit of a parabolic-elliptic-parabolic system for ion transport networks ⋮ On a singularly perturbed semi-linear problem with Robin boundary conditions ⋮ Nonlinear stability of planar traveling waves in a chemotaxis model of tumor angiogenesis with chemical diffusion ⋮ A reducing mechanism on wave speed for chemotaxis systems with degenerate diffusion ⋮ Convergence to traveling waves of a singular PDE-ODE hybrid chemotaxis system in the half space ⋮ Convergence to nonlinear diffusion waves for a hyperbolic-parabolic chemotaxis system modelling vasculogenesis ⋮ Saturation of the signal on the boundary: global weak solvability in a chemotaxis-Stokes system with porous-media type cell diffusion ⋮ Global weak solutions and asymptotics of a singular PDE-ODE chemotaxis system with discontinuous data ⋮ Global stability under dynamic boundary conditions of a nonlinear PDE model arising from reinforced random walks

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the ill-posedness of the Prandtl equations in three-dimensional space
• Asymptotic stability of traveling waves of a chemotaxis model with singular sensitivity
• Asymptotic nonlinear stability of traveling waves to conservation laws arising from chemotaxis
• Boundary layers for compressible Navier-Stokes equations with density-dependent viscosity and cylindrical symmetry
• Boundary layers in parabolic perturbations of scalar conservation laws
• Boundary layer problem on a hyperbolic system arising from chemotaxis
• Initiation of slime mold aggregation viewed as an instability
• Model for chemotaxis
• Traveling bands of chemotactic bacteria: a theoretical analysis
• Global solutions of some chemotaxis and angiogenesis system in high space dimension
• A chemotactic model for the advance and retreat of the primitive streak in avian development
• Asymptotic dynamics on a singular chemotaxis system modeling onset of tumor angiogenesis
• A user's guide to PDE models for chemotaxis
• Transient behavior of a chemotaxis system modelling certain types of tissue inflammation
• Boundary movement of chemotactic bacterial populations
• Model and analysis of chemotactic bacterial patterns in a liquid medium
• Boundary layers for viscous perturbations of noncharacteristic quasilinear hyperbolic problems
• From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I
• On the global existence of solutions to the Prandtl's system.
• Mathematical biology. Vol. 1: An introduction.
• Stability of planar traveling waves in a Keller-Segel equation on an infinite strip domain
• Characteristic boundary layers in real vanishing viscosity limits
• A model of wound-healing angiogenesis in soft tissue
• A chemotaxis model motivated by angiogenesis
• Cellular pattern formation during Dictyostelium aggregation
• Steadily propagating waves of a chemotaxis model
• Global well-posedness for a multidimensional chemotaxis model in critical Besov spaces
• Mathematics of traveling waves in chemotaxis
• Large-time behavior of a parabolic-parabolic chemotaxis model with logarithmic sensitivity in one dimension
• Global dynamics and diffusion limit of a one-dimensional repulsive chemotaxis model
• Boundary layers for the Navier-Stokes equations of compressible fluids
• Global well-posedness and zero diffusion limit of classical solutions to 3D conservation laws arising in chemotaxis
• The inviscid limit of the incompressible anisotropic Navier-Stokes equations with the non-slip boundary condition
• Well-posedness of a 3D parabolic-hyperbolic Keller-Segel system in the Sobolev space framework
• Initial-boundary value problems for a system of hyperbolic balance laws arising from chemotaxis
• Considerations regarding the mathematical basis for Prandtl's boundary layer theory
• The two-dimensional Keller–Segel system with singular sensitivity and signal absorption: Global large-data solutions and their relaxation properties
• Global Dynamics of a Hyperbolic-Parabolic Model Arising from Chemotaxis
• Stability of traveling waves of the Keller–Segel system with logarithmic sensitivity
• Quantitative decay of a one-dimensional hybrid chemotaxis model with large data
• Nonlinear Stability of Traveling Waves to a Hyperbolic-Parabolic System Modeling Chemotaxis
• NONLINEAR STABILITY OF LARGE AMPLITUDE VISCOUS SHOCK WAVES OF A GENERALIZED HYPERBOLIC–PARABOLIC SYSTEM ARISING IN CHEMOTAXIS
• ON A HYPERBOLIC–PARABOLIC SYSTEM MODELING CHEMOTAXIS
• Global existence of solutions to a hyperbolic-parabolic system
• On the vanishing viscosity limit for the 3D Navier-Stokes equations with a slip boundary condition
• Infinite time aggregation for the critical Patlak‐Keller‐Segel model in ℝ²
• On the ill-posedness of the Prandtl equation
• Zero-viscosity limit of the linearized Navier-Stokes equations for a compressible viscous fluid in the half-plane
• A System of Reaction Diffusion Equations Arising in the Theory of Reinforced Random Walks
• Aggregation, Blowup, and Collapse: The ABC's of Taxis in Reinforced Random Walks
• Vanishing Shear Viscosity in the Equations of Compressible Fluids for the Flows with the Cylinder Symmetry
• Asymptotic and viscous stability of large-amplitude solutions of a hyperbolic system arising from biology
• Well-posedness of the Prandtl equation in Sobolev spaces
• Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues
• Zero-Viscosity Limit of the Linearized Compressible Navier-Stokes Equations with Highly Oscillatory Forces in the Half-Plane
• Viscous boundary layers in hyperbolic-parabolic systems with Neumann boundary conditions
• A mathematical model for the roles of pericytes and macrophages in the initiation of angiogenesis. I: The role of protease inhibitors in preventing angiogenesis
• Boundary layer stability in real vanishing viscosity limit