Chemotactic collapse for the Keller-Segel model

Journal of Mathematical Biology

Volumn 35, Issue 2, 1996, Pages 177-194

  Herrero, Miguel A ^a   Velázquez, Juan J L ^a  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

Advection diffusion systems; Asymptotic behaviour; Blow up; Chemotaxis; Matched asymptotic expansions

Indexed keywords

ARTICLE; BIOLOGICAL MODEL; CHEMOTAXIS; MATHEMATICS; PHYSIOLOGY;

CHEMOTAXIS; MATHEMATICS; MODELS, BIOLOGICAL;

EID: 0030334089     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s002850050049     Document Type: Article

References (13)

1. [AV] S. B. Angenent and J. J. L. Velázquez, Asymptotic shape of cusp singularities in curve shortening. Duke Math. Journal 77(1) (1995) 71-110
2. [AY] Adimurthi and S. L. Yadava, Existence and nonexistence of positive radial solutions of Neumann problems with critical Sobolev exponents. Archive Rat. Mech. Anal. 115 (1991) 275-296
3. [CP] S. Childress and J. K. Percus, Nonlinear aspects of chemotaxis. Math. Biosci. 56 (1981) 217-237
4. [GK] Y. Giga and R. V. Kohn, Asymptotically self-similar blow-up of semilinear heat equations. Comm. Pure Appl. Math. 38 (1985) 297-319
5. [JL] W. Jäger and S. Luckhaus, On explosions of solutions to a system of partial differential equations modelling chemotaxis. Trans. Amer. Math. Soc. vol. 239, n° 2 (1992) 819-824
6. [HV1] M. A. Herrero and J. J. L. Velázquez, Singularity patterns in a chemotaxis model. To appear in Mathematische Annalen
7. [HV2] M. A. Herrero and J. J. L. Velázquez, On the melting of ice balls. To appear in SIAM Journal of Mathematical Analysis
8. [HV3] M. A. Herrero and J. J. L. Velázquez, Explosion de solutions d'equations paraboliques semilineaires supercritiques. C.R. Acad. Sci. Paris, t. 319, Serie I (1994) 141-145
9. [KS] E. F. Keller and L. A. Segel, Initiation of slime mold aggregation viewed as an instability. J. Theor. Biol. 26 (1970) 399-415
10. [LNT] C. S. Lin, W. M. Ni and I. Takagi, Large amplitude stationary solutions to a chemotaxis system. Journal of Differential Equations 72, 1 (1988) 1-23
11. [N] T. Nagai, Blow-up of radially symmetric solutions to a chemotaxis system. Adv. Math. Sci. and Appl. (1995) 1-21
12. [Na] V. Nanjundiah, Chemotaxis, signal relaying and aggregation morphology. J. Theor. Biol. 42 (1973) 63-105
13. [V] J. J. L. Velázquez, Curvature blow-up in perturbations of minimal cones evolving by mean curvature flow. Annali Scuola Normale Superiore di Pisa, Serie IV, vol. XXI, Fasc. 4 (1994) 595-628