Stationary solutions of chemotaxis systems-Reference-Cited by-同舟云学术

Stationary solutions of chemotaxis systems

Published:1985 Issue:2 Volume:292 Page:531-556
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Schaaf Renate

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1985-292-02/S0002-9947-1985-0808736-1/S0002-9947-1985-0808736-1.pdf

Reference21 articles.

1. Global and local behavior of bifurcating multidimensional continua of solutions for multiparameter nonlinear eigenvalue problems;Alexander, J. C.;Arch. Rational Mech. Anal.,1981

2. Biased random walk models for chemotaxis and related diffusion approximations;Alt, Wolfgang;J. Math. Biol.,1980

3. Orientation of cells migrating in a chemotactic gradient;Alt, Wolfgang,1980

4. A bifurcation problem for a nonlinear partial differential equation of parabolic type;Chafee, N.;Applicable Anal.,1974

5. Nonlinear aspects of chemotaxis;Childress, S.;Math. Biosci.,1981

Cited by 96 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Global existence and finite-time blowup for a mixed pseudo-parabolic r(x)-Laplacian equation;Advances in Nonlinear Analysis;2024-01-01

2. A bifurcation result for a Keller-Segel-type problem;Fractional Calculus and Applied Analysis;2023-11-16

3. Global existence and finite time blowup for a mixed pseudo-parabolic p-Laplacian type equation;Nonlinear Analysis: Real World Applications;2023-10

4. Analysis of a mathematical model of the aggregation process of cellular slime mold within the frame of fractional calculus;International Journal of Modelling and Simulation;2023-08-27

5. Stability Arguments in Molecular Communication Networks;Bifurcation Theory and Applications [Working Title];2023-08-11