WAVES FOR A HYPERBOLIC KELLER–SEGEL MODEL AND BRANCHING INSTABILITIES

DOI10.1142/S0218202511005386zbMath1221.35088OpenAlexW2116543944WikidataQ60502806 ScholiaQ60502806MaRDI QIDQ3005973

Fiammetta Cerreti, Perthame, Benoît, Nicolas Vauchelet, Min Tang, Christian Schmeiser

Publication date: 10 June 2011

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218202511005386

zbMATH Keywords

cell proliferationswarming behaviourbranching patterns

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Initial value problems for first-order hyperbolic systems (35L45) Cell movement (chemotaxis, etc.) (92C17) Traveling wave solutions (35C07)

Related Items (10)

ON THE ASYMPTOTIC THEORY FROM MICROSCOPIC TO MACROSCOPIC GROWING TISSUE MODELS: AN OVERVIEW WITH PERSPECTIVES ⋮ ON THE MATHEMATICAL THEORY OF THE DYNAMICS OF SWARMS VIEWED AS COMPLEX SYSTEMS ⋮ Cooperation, competition, organization: The dynamics of interacting living populations ⋮ Emergence of spatial patterns in a mathematical model for the co-culture dynamics of epithelial-like and mesenchymal-like cells ⋮ On the mathematical theory of living systems. I: Complexity analysis and representation ⋮ Singular patterns in Keller–Segel-type models ⋮ Mathematical models of cell self-organization ⋮ MATHEMATICS AND COMPLEXITY IN BIOLOGICAL SCIENCES ⋮ ON THE DIFFICULT INTERPLAY BETWEEN LIFE, "COMPLEXITY", AND MATHEMATICAL SCIENCES ⋮ Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues

Cites Work

• A user's guide to PDE models for chemotaxis
• Mathematical biology. Vol. 1: An introduction.
• Asymptotic analysis of an advection-dominated chemotaxis model in multiple spatial dimensions
• Nonlinear Stability of Traveling Waves to a Hyperbolic-Parabolic System Modeling Chemotaxis
• A MACROSCOPIC CROWD MOTION MODEL OF GRADIENT FLOW TYPE
• A Classification of Spikes and Plateaus
• Reaction–diffusion modelling of bacterial colony patterns
• Boundedness in the Higher-Dimensional Parabolic-Parabolic Chemotaxis System with Logistic Source
• Models of Self-Organizing Bacterial Communities and Comparisons with Experimental Observations
• The Keller–Segel Model for Chemotaxis with Prevention of Overcrowding: Linear vs. Nonlinear Diffusion
• The Keller--Segel Model with Logistic Sensitivity Function and Small Diffusivity

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