Parabolic models for chemotaxis on weighted networks

DOI10.1016/j.matpur.2017.07.003zbMath1370.92028arXiv1511.07279OpenAlexW2962732123MaRDI QIDQ2404480

Fabio Camilli, Lucilla Corrias

Publication date: 19 September 2017

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.07279

zbMATH Keywords

networkchemotaxisheat kerneltransmission conditions

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Cell movement (chemotaxis, etc.) (92C17) Systems biology, networks (92C42) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)

Related Items (14)

Kinetic Layers and Coupling Conditions for Macroscopic Equations on Networks I: The Wave Equation ⋮ Nonlinear flux-limited models for chemotaxis on networks ⋮ Asymptotic convergence of solutions of Keller-Segel equations in network shaped domains ⋮ Mathematical analysis of parabolic models with volume-filling effect in weighted networks ⋮ Multi-spike patterns for the Gierer-Meinhardt model with heterogeneity on \(Y\)-shaped metric graph ⋮ Chemotaxis on networks: Analysis and numerical approximation ⋮ Stationary solutions and asymptotic behaviour for a chemotaxis hyperbolic model on a network ⋮ Kinetic and Moment Models for Cell Motion in Fiber Structures ⋮ Concentration phenomena on \(Y\)-shaped metric graph for the Gierer-Meinhardt model with heterogeneity ⋮ Existence of multi-peak solutions to the Schnakenberg model with heterogeneity on metric graphs ⋮ Global solutions for a chemotaxis hyperbolic-parabolic system on networks with nonhomogeneous boundary conditions ⋮ Kinetic and related macroscopic models for chemotaxis on networks ⋮ Local and global solutions for a hyperbolic–elliptic model of chemotaxis on a network ⋮ Stability analysis of spike solutions to the Schnakenberg model with heterogeneity on metric graphs

Cites Work

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• Initiation of slime mold aggregation viewed as an instability
• Model for chemotaxis
• A user's guide to PDE models for chemotaxis
• Elliptic operators on elementary ramified spaces
• The spread of the potential on a homogeneous tree
• A review of mathematical models for the formation of vascular networks
• A mathematical model for adaptive transport network in path finding by true slime mold
• Existence, uniqueness and asymptotic behavior of the solutions to the fully parabolic Keller-Segel system in the plane
• Semigroup methods for evolution equations on networks
• Gaussian estimates for a heat equation on a network
• Wave propagation, observation and control in 1-\(d\) flexible multi-structures.
• Variational and semigroup methods for waves and diffusion in networks
• THE SCALAR KELLER–SEGEL MODEL ON NETWORKS
• The one-dimensional chemotaxis model: global existence and asymptotic profile
• Global Smooth Solutions for a Hyperbolic Chemotaxis Model on a Network
• L^PBounds of solutions of reaction-diffusion equations

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