Finite-time aggregation into a single point in a reaction-diffusion system

Nonlinearity

Volumn 10, Issue 6, 1997, Pages 1739-1754

  Herrero, M A ^a   Medina, E ^b   Velazquez J J L ^a  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^b UNIVERSITY OF CÁDIZ   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000507343     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/10/6/016     Document Type: Article

References (17)

1. Andreucci D, Herrero M A and Velázquez J J L 1997 Liouville theorems and blow-up behaviour in semilinear reaction-diffusion systems Ann. l'Institute Henri Poincaré 14 1-53
2. Angenent S B and Velázquez J J L 1995 Asymptotic shape of cusp singularities in curve shortening Duke Math. J. 77 71-110
3. Childress S and Percus J K 1981 Nonlinear aspects of chemotaxis Math. Boisc. 56 217-37
4. Escobedo M, Herrero M A and Velázquez J J L 1996 A nonlinear Fokker-Planck equation modelling the approach to thermal equilibrium in a homogeneous plasma Trans. Amer. Maths Soc. submitted
5. p Comm. Pure Appl. Math. 45 821-69
6. Jäger W and Luckhaus S 1992 On explosions of solutions to a system of partial differential equations modelling chemotaxis Trans. Am. Math. Soc. 329 819-24
7. Keller E F and Segel L A 1970 Initiation of slime mold aggregation viewed as an instability J. Theor. Biol. 26 399-415
8. Herrero M A and Velázquez J J L 1996 Singularity patterns in a chemotaxis model Math. Ann. 306 583-623
9. Herrero M A and Velázquez J J L 1996 Chemotactic collapse for the Keller-Segel model J. Math. Biol. 35 177-96
10. Herrero M A and Velázquez J J L A blow-up mechanism for a chemotaxis model Ann. Scuola Normale Sup. Pisa. to appear
11. Nagai T 1995 Blow-up of radially symmetric solutions to a chemotaxis system Adv. Math. Sci. Appl. 1-21
12. Nanjundiah V 1973 Chemotaxis, signal relaying and aggregation morphology J. Theor. Biol. 42 63-105
13. Velázquez J J L 1993 Classification of singularities for blowing-up solutions in higher dimensions Trans. Am. Math. Soc. 338 441-64
14. Velázquez J J L 1992 Higher dimensional blow-up for semilinear parabolic equations Commun. PDE 17 1567-96
15. Velázquez J J L 1994 Curvature blow-up in perturbations of minimal cones evolving by mean curvature flow Annali Scuola Normale Sup. Pisa 21 595-628
16. Wolansky G 1992 On steady distributions of self-attracting clusters under friction and fluctuations Arch. Rational Mech. Anal. 119 355-91
17. Wolansky G 1992 On the evolution of self-interacting clusters and applications to semilinear equations with exponential nonlinearity J. Anal. Math. 59 251-72