Qualitative Behavior of a Keller–Segel Model with Non-Diffusive Memory

DOI10.1080/03605300903473400zbMath1193.35013OpenAlexW2102409243MaRDI QIDQ3550971

Kyungkeun Kang, Angela Stevens, Juan J. L. Velazquez

Publication date: 8 April 2010

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605300903473400

zbMATH Keywords

periodic boundary conditionsone space dimensionnon-diffusive chemoattractantlogarithmic chemotactic sensitivitypartially diffusive system

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Reaction-diffusion equations (35K57) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Asymptotic expansions of solutions to PDEs (35C20) Cell movement (chemotaxis, etc.) (92C17) Blow-up in context of PDEs (35B44)

Related Items (9)

ON THE ASYMPTOTIC THEORY FROM MICROSCOPIC TO MACROSCOPIC GROWING TISSUE MODELS: AN OVERVIEW WITH PERSPECTIVES ⋮ Bounded global solutions to a Keller-Segel system with nondiffusive chemical in \(\mathbb{R}^{n}\) ⋮ Global asymptotic stability in a chemotaxis-growth model for tumor invasion ⋮ Singular structure formation in a degenerate haptotaxis model involving myopic diffusion ⋮ Ant foraging and geodesic paths in labyrinths: analytical and computational results ⋮ On a Keller-Segel system with logarithmic sensitivity and non-diffusive chemical ⋮ Global solutions to a chemotaxis system with non-diffusive memory ⋮ Stabilization in a chemotaxis model for tumor invasion ⋮ Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues

Cites Work

• Unnamed Item
• Unnamed Item
• Traveling bands of chemotactic bacteria: a theoretical analysis
• Elliptic partial differential equations of second order
• Singularity patterns in a chemotaxis model
• On Existence of Global Solutions and Blow-Up to a System of Reaction-Diffusion Equations Modelling Chemotaxis
• 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

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