Stability of constant steady states and existence of unbounded solutions in time to a reaction--diffusion equation modelling chemotaxis

DOI10.1016/j.na.2003.11.014zbMath1083.35018OpenAlexW2002387039MaRDI QIDQ1883459

Tatsuyuki Nakaki, Toshitaka Nagai

Publication date: 12 October 2004

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2003.11.014

zbMATH Keywords

Neumann boundary conditionsone space-dimension

Mathematics Subject Classification ID

Related Items (1)

Existence of solutions to a new model of biological pattern formation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Chemotactic collapse for the Keller-Segel model
• Initiation of slime mold aggregation viewed as an instability
• Semigroups of linear operators and applications to partial differential equations
• Geometric theory of semilinear parabolic equations
• Nonlinear aspects of chemotaxis
• Sur une équation intégro-différentielle non linéaire issue de la biologie
• Symmetrization techniques on unbounded domains: Application to a chemotaxis system on \(\mathbb{R}^N\)
• Blow-up in a chemotaxis model without symmetry assumptions
• On Existence of Global Solutions and Blow-Up to a System of Reaction-Diffusion Equations Modelling Chemotaxis
• Stationary Solutions of Chemotaxis Systems
• L^PBounds of solutions of reaction-diffusion equations
• On Explosions of Solutions to a System of Partial Differential Equations Modelling Chemotaxis
• Global Behaviour of a Reaction-Diffusion System 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
• Chemotactic collapse in a parabolic system of mathematical biology
• Chemotactic collapse in a parabolic-elliptic system of mathematical biology
• Concentration lemma, Brezis-Merle type inequality, and a parabolic system of chemotaxis

This page was built for publication: Stability of constant steady states and existence of unbounded solutions in time to a reaction--diffusion equation modelling chemotaxis