Bibliography

1

P. Biler, W. Hebisch, and T. Nadzieja, The Debye system: Existence and large time behavior of solutions, Nonlinear Anal. 238 (1994), 1189-1209.

2

H. Brezis, Analyse fonctionnelle, théorie et applications, Masson, Paris, 1983.

3

A. Eden, C. Foias, B. Nicolaenko, and R. Temam, Ensembles inertiels pour des équations d'évolution dissipatives, C. R. Acad. Sci. Paris 310 (1990), 559-562.

4

A. Eden, C. Foias, B. Nicolaenko, and R. Temam, Exponential attractors for dissipative evolution equations, Research in Applied Mathematics, vol. 37, John-Wiley and Sons, New York, 1994.

5

A. Friedman, Partial Differential Equations, Holt, Rinehart and Winston, New York, 1969.

6

H. Gajewski and K. Zacharias, Global behavior of a reaction-diffusion system modeling chemotaxis, Math. Nachr. 195 (1998), 77-114.

7

M. A. Herrero and J. J. L. Velázquez, A blow-up mechanism for a chemotaxis model, Ann. Scoula Norm. Sup. Pisa IV 35 (1997), 633-683.

8

D. Horstmann and G. Wang, Blowup in a chemotaxis model without symmetry assumptions, preprint.

9

E. F. Keller and L. A. Segel, Initiation of slime mold aggregation viewed as instability, J. theor. Biol. 26 (1970), 399-415.

10

I. R. Lapidus and M. Levandowsky, Modeling chemosensory responses of swimming eukaryotes, Biological Growth and Spread, Proceedings, Heidelberg, Lecture Notes in Biomathematics 38 (1979).

11

J. L. Lions and E. Magenes, Problems aux limites non homogenes et apolications, vol. 1, Dunod, Paris, 1968.

12

T. Nagai, T. Senba, and T. Suzuki, Chemotaxis collapse in a parabolic system of mathematical biology, preprint.

13

T. Nagai, T. Senba, and K. Yoshida, Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis, Funkcialaj Ekvacioj 40 (1997), 411-433.

14

W.-M. Ni and I. Takagi, Locating the peaks of least-energy solutions to a semilinear Neumann problem, Duke Math. J. 70 (1993), 247-281.

15

M. H. Protter and H. F. Weinberger, Maximal principles in differential equations, Prentice-Hall, 1967.

16

S.-U. Ryu and A. Yagi, Optimal control of Keller-Segel equations, submitted.

17

R. Schaaf, Stationary solutions of chemotaxis systems, Trans. Amer. Math. Soc. 292 (1985), 531-556.

18

T. Senba and T. Suzuki, Some structures of the solution set for a stationary system of chemotaxis, Adv. Math. Sci. Appl., to appear.

19

H. Tanabe, Equations of Evolution, Pitman, 1979.

20

H. Tanabe, Functional analytic methods for partial diffrential equations, Monographs and textbooks in pure and applied mathematics, vol. 204, Marcel-Dekker, Inc., 1997.

21

R. Temam, Infinite-dimensional dynamical systems in mechanics and physics, second edition, Applied mathematical sciences, vol. 68, Springer-Verlag, New York, 1997.

22

H. Wiebers, S-shaped bifurcation curves of nonlinear elliptic boundary value problems, Math. Ann. 270 (1985), 555-570.

23

A. Yagi, Norm behavior of solutions to the parabolic system of chemotaxis, Math. Japonica 45 (1997), 241-265.