Stationary Solutions of Chemotaxis Systems
- 1 December 1985
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 292 (2) , 531-556
- https://doi.org/10.2307/2000228
Abstract
The Keller-Segel Model is a system of partial differential equations modelling a mutual attraction of amoebae caused by releasing a chemical substance (Chemotaxis). This paper analyzes the stationary solutions of the system with general nonlinearities via bifurcation techniques and gives a criterion for bifurcation of stable nonhomogeneous aggregation patterns. Examples are discussed with various kinds of nonlinearities modelling the sensitivity of the chemotaxis response.Keywords
This publication has 13 references indexed in Scilit:
- Maximum Principles in Differential EquationsPublished by Springer Nature ,1984
- Global behaviour of solution branches for some Neumann problems depending on one or several parameters.Journal für die reine und angewandte Mathematik (Crelles Journal), 1984
- Global and local behavior of bifurcating multidimensional continua of solutions for multiparameter nonlinear eigenvalue problemsArchive for Rational Mechanics and Analysis, 1981
- Nonlinear aspects of chemotaxisMathematical Biosciences, 1981
- Biased random walk models for chemotaxis and related diffusion approximationsJournal of Mathematical Biology, 1980
- Modeling Chemosensory Responses of Swimming EukaryotesPublished by Springer Nature ,1980
- Orientation of Cells Migrating in a Chemotactic GradientPublished by Springer Nature ,1980
- On the Lyapunov-stability of stationary solutions of semilinear parabolic differential equationsJournal of Differential Equations, 1976
- A bifurcation problem for a nonlinear partial differential equation of parabolic type†Applicable Analysis, 1974
- Some global results for nonlinear eigenvalue problemsJournal of Functional Analysis, 1971