Global existence of solutions to a parabolic system for chemotaxis in two space dimensions

Nonlinear Analysis, Theory, Methods and Applications

Volumn 30, Issue 8, 1997, Pages 5381-5388

  Nagai, Toshitaka ^a  

^a KYUSHU INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

Chemotaxis system; Global existence; Parabolic system; The Trudinger Moser inequality

Indexed keywords

EID: 0042727055     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(97)00395-7     Document Type: Article

References (18)

1. p bounds of solutions of reaction-diffusion equations, Comm. Partial Differential Equations, 4, 827-868 (1979).
2. BILER P. & NADZIEJA T., Existence and nonexistence of solutions for a model of gravitational interactions of particles, I, Colloq. Math, 66, 319-334 (1994).
3. BILER P, HEBISCH W. & NADZIEJA T., The Debye system : Existence and large time behavior of solutions, Nonlinear Anal., 238, 1189-1209 (1994).
4. BILER P., Existence and nonexistence of solutions for a model of gravitational interactions of particles, III, Colloq. Math., 68, 229-239 (1995).
5. 2, J. Differential Geom., 27, 259-296 (1988).
6. CHILDRESS S., Chemotactic collapse in two dimensions, Lecture Notes in Biomath., vol. 55, Springer, Berlin-Heidelberg-New York, 61-66 (1984).
7. CHILDRESS S. & PERCUS J. K., Nonlinear aspects of chemotaxis, Math. Biosci., 56, 217-237 (1981).
8. HENRY D., Geometric Theory of Semilinear Parabolic Equations, Lecture Note in Math., 840, Springer, 1981.
9. HERRERO M. A. & VELAZQUEZ J. J. L., Singularity patterns in a chemotaxis model, Math. Ann., to appear.
10. HERRERO M. A. & VELAZQUEZ J. J. L., Chemotaxis collapse for the Keller-Segel model, J. Math. Biol., to appear.
11. HERRERO M. A. & VELAZQUEZ J. J. L., A blow up mechanism for a chemotaxis model, preprint.
12. JAGER W. & LUCKHAUS S., On explosions of solutions to a system of partial differential equations modelling chemotaxis, Trans. Amer. Math. Soc., 329, 819-824 (1992).
13. KELLER E. F. & SEGEL L. A., Initiation of slime mold aggregation viewed as an instability, J. Theor. Biol., 26, 399-415 (1970).
14. MOSER J., A sharp form of an inequality by N. Trudinger, Indiana Univ. Math. J., 20, 1077-1092 (1971).
15. NAGAI T., Blow-up of radially symmetric solutions to a chemotaxis system, Adv. Math. Sci. Appl., 5, 581-601 (1995).
16. NAGAI T., SENBA T. & YOSHIDA K., Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis, preprint.
17. TRUDINGER N. S., On imbeddings into Orlicz spaces and some applications, J. Math. Mech., 17, 473-483 (1967).
18. YAGI A., Norm behavior of solutions to the parabolic system of chemotaxis, Math. Japonica, to appear.