Metastability in chemotaxis models

Journal of Dynamics and Differential Equations

Volumn 17, Issue 2, 2005, Pages 293-330

  Potapov, A B ^a   Hillen, T ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Chemotaxis; Metastability; Transients; Volume filling

Indexed keywords

EID: 21244493212     PISSN: 10407294     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10884-005-2938-3     Document Type: Article

References (16)

1. Alikakos, N., Bates, P. W., and Fusco, P. (1991). Slow motion for the Cahn-Hilliard equation in one space dimension. J. Differential Equations 90, 81-135.
2. Crutchfield, J. P., and Kaneko, K. (1998). Are attractors relevant to turbulence? Phys. Rev. Lett. 60, 2715-2718.
3. Dolak, Y., and Hillen, T. (2003). Cattaneo models for chemotaxis, numerical solution and pattern formation. J. Math. Biol. 46(2), 153-170.
4. Dolak, Y., and Schmeiser, C. (2004). The Keller-Segel model with small diffusion. ANUM-Preprint, 10/04, 1-22.
5. Grinfeld, M., and Novick-Cohen, A. (1999). The viscous Cahn-Hilliard equation: Morse decomposition and structure of the global attractor. Trans. Am. Math. Soc. 351(6), 2375-2406.
6. Hillen, T., and Painter, K. (2001). Global existence for a parabolic chemotaxis model with prevention of overcrowding. Adv. Appl. Math. 26(4), 280-301.
7. Horstmann, D. (2003). From 1970 until present: The Keller-Segel model in chemotaxis and its consequences I. Jahresbericht der DMV 105(3), 103-165.
8. Horstmann, D. (2004). From 1970 until present: The Keller-Segel model in chemotaxis and its consequences II. Jahresbericht der DMV 106(2), 51-69.
9. Iron, D., and Ward, J. (2004). The stability and dynamics of hot-spot solutions for two one-dimensional microwave heating models. Anal. Appl. 2(1), 21-77.
10. Keller, E. F., and Segel, L. A. (1971). Model for chemotaxis. J. Theor. Biol. 30, 225-234.
11. Murray, J. D. (1989). Mathematical Biology, Springer, Berlin.
12. Painter, K., and Hillen, T. (2002). Volume-filling and quorum-sensing in models for chemosensitive movement. Can. Appl. Math. Q. 10(4), 501-543.
13. Patlak, C. S. (1953). Random walk with persistence and external bias. Bull. Math. Biophys. 15, 311-338.
14. Schaaf, R. (1985). Stationary solutions of chemotaxis systems. Trans. AMS 292(2), 531-556.
15. Sleeman B. D., Ward M. J., and Wei J. C. (2005). The Existence and Stability of Spike Patterns in a Chemotaxis Model. SIAM J. Appl. Math. 65(3), 790-817.
16. Sun, X., and Ward, M. (2000). Dynamics and coarsening of interfaces for the viscous Cahn-Hilliard equation in one spatial dimension. Stud. Appl. Math. 105, 203-234.