Qualitative behavior of solutions of chemotactic diffusion systems: Effects of motility and chemotaxis and dynamics

SIAM Journal on Mathematical Analysis

Volumn 31, Issue 3, 2000, Pages 535-560

  Wang, Xuefeng ^a  

^a Tulane University   (United States)

Author keywords

Bifurcation; Blowup; Chemotaxis; Concentration; Decay rates; Existence and uniqueness; Global boundedness; Helly's theorem; Monotonicity; Moser Alikakos iteration; Motility; Stability

Indexed keywords

EID: 0034376967     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141098339897     Document Type: Article

References (14)

1. p bounds of solutions of reaction-diffusion equations, Comm. Partial Differential Equations, 4 (1979), pp. 827-868.
2. H. AMANN, Dynamic theory of quasilinear parabolic equations II: Reaction-diffusion systems, Differential Integral Equations, 3 (1990), pp. 13-75.
3. H. AMANN, Dynamic theory of quasilinear parabolic systems III: Global existence, Math. Z., 202 (1989), pp. 219-250.
4. J. BLAT AND K. J. BROWN, Global bifurcation of positive solutions in some systems of elliptic equations, SIAM J. Math. Anal., 17 (1986), pp. 1339-1353.
5. M. G. CRANDALL AND P. H. RABINOWITZ, Bifurcation from simple eigenvalues, J. Funct. Anal., 8 (1971), pp. 321-340.
6. A.-K. DRANGEID, The principle of linearized stability for quasilinear parabolic evolution equations, Nonlinear Anal., 13 (1989), pp. 1091-1113.
7. D. HENRY, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math. 840, Springer-Verlag, Berlin, Heidelberg, New York, 1981.
8. E. F. KELLER AND L. A. SEGEL, Initiation of slime mold aggregation viewed as an instability, J. Theoret. Biol., 26 (1970), pp. 399-415.
9. O. A. LADYZENSKAYA, V. A. SOLONNIKOV, AND N. N. URALCEVA, Linear and Quasilinear Equations of Parabolic Type, Transl. Math. Monogr. 23, American Mathematical Society, Providence, RI, 1967.
10. D. LAUFFENBURGER, R. ARIS, AND K. KELLER, Effects of cell motility and chemotaxis on microbial population growth, Biophys. J., 40 (1982), pp. 209-219.
11. W. K. PILGRAM AND F. D. WILLIAMS, Survival value of chemotaxis in mixed cultures, Canad. J. Microbiol., 22 (1976), pp. 1771-1773.
12. P. H. RABINOWITZ, Some global results for nonlinear eigenvalue problems, J. Funct. Anal., 7 (1971), pp. 487-513.
13. G. SIMONETT, Center manifolds for quasilinear reaction-diffusion systems, Differential Integral Equations, 8 (1995), pp. 753-796.
14. B. ZENG, Steady states of a chemotaxis system, Appl. Math., 1 (1990), pp. 78-83 (in Chinese) .