Qualitative analysis on a chemotactic diffusion model for two species competing for a limited resource
Authors:
Xuefeng Wang and Yaping Wu
Journal:
Quart. Appl. Math. 60 (2002), 505-531
MSC:
Primary 35Q80; Secondary 35K50, 35K57, 92C17, 92D25
DOI:
https://doi.org/10.1090/qam/1914439
MathSciNet review:
MR1914439
Full-text PDF Free Access
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Additional Information
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D. Lauffenburger and P. Calcano, Competition between two microbial populations in a non-mixed environment: Effect of cell random motility, Biotech. and Bioengrg. 25, 2103–2125 (1983)
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J. Blat and K. Brown, Global bifurcation of positive solutions in some systems of elliptic equations, SIAM J. Math. Anal. 17, 1339–1353 (1986)
M. Crandall and P. Rabinowitz, Bifurcation, perturbation of simple eigenvalues and linearized stability, Arch. Rational Mech. Anal. 52, 161–180 (1973)
A.-K. Drangeid, The principle of linearized stability for quasilinear parabolic evolution equations, Nonlinear Anal. 13, 1091–1113 (1989)
J. Dockery, V. Hutson, K. Mischaikow, and M. Pernarowski, The evolution of slow dispersal rates: A reaction diffusion model, J. Math. Biol. 37 61–83 (1998)
D. Lauffenburger, R. Aris, and K. Keller, Effects of cell motility and chemotaxis on microbial population growth, J. Biophys. Soc. 40, 209–219 (1982)
D. Lauffenburger and P. Calcano, Competition between two microbial populations in a non-mixed environment: Effect of cell random motility, Biotech. and Bioengrg. 25, 2103–2125 (1983)
P. Rabinowitz, Some global results for nonlinear eigenvalue problems, J. Functional Analysis 7, 487–513 (1971)
G. Simonett, Center manifolds for quasilinear reaction-diffusion systems, Differential Integral Equations 8, 753–796 (1995)
X.-F. Wang, Qualitative behavior of solutions of chemotactic diffusion systems: Effects of motility and chemotaxis and dynamics, SIAM J. Math. Anal. 31 535–560 (2000)
B. Zeng, Steady state solutions to a model for chemotaxis, Math. Appl. 3, 78–83 (1990) (in Chinese)
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© Copyright 2002
American Mathematical Society
