Type II blowup of solutions to a simplified Keller-Segel system in two dimensional domains

Nonlinear Analysis, Theory, Methods and Applications

Volumn 66, Issue 8, 2007, Pages 1817-1839

  Senba, Takasi ^a  

^a UNIVERSITY OF MIYAZAKI   (Japan)

Author keywords

Blowup; Keller Segel system; Nagai system; Parabolic elliptic system; Type II

Indexed keywords

BOUNDARY CONDITIONS; FINITE ELEMENT METHOD; FUNCTION EVALUATION;

KELLER-SEGEL SYSTEMS; NAGAI SYSTEMS; PARABOLIC-ELLIPTIC SYSTEMS; TYPE II BLOWUP;

LINEAR SYSTEMS;

EID: 33846676393     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2006.02.027     Document Type: Article

References (9)

1. Herrero M.A., and Velázquez J.J.L. A blow-up mechanism for a chemotaxis model. Ann. Sc. Norm. Super. Pisa IV 35 (1997) 633-683
2. Keller E.F., and Segel L.A. Initiation of slime mold aggregation viewed as an instability. J. Theoret. Biol. 26 (1970) 399-415
3. Nagai T. Blow-up of radially symmetric solutions to a chemotaxis system. Adv. Math. Sci. Appl. 5 (1995) 581-601
4. Nagai T. Blow-up of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains. J. Inequal. Appl. 6 (2001) 37-55
5. Nanjundiah V. Chemotaxis, signal relaying, and aggregation morphology. J. Theoret. Biol. 42 (1973) 63-105
6. Senba T., and Suzuki T. Chemotactic collapse in a parabolic-elliptic system of mathematical biology. Adv. Differential Equations 6 (2001) 21-50
7. Senba T., and Suzuki T. Parabolic system of chemotaxis: blowup in a finite and the infinite time. Met. Appl. Ana. 8 (2001) 349-368
8. Senba T., and Suzuki T. Blowup behavior of solutions to rescaled Jäger-Luckhaus system. Adv. Differential Equations 8 (2003) 787-820
9. Suzuki T. Free Energy and Self-Interacting Particles (2005), Birkhäuser, Boston