an:01529805
Zbl 0999.35031
Senba, Takasi; Suzuki, Takashi
Some structures of the solution set for a stationary system of chemotaxis
EN
Adv. Math. Sci. Appl. 10, No. 1, 191-224 (2000).
00062313
2000
j
35J65 47J30 35J20
Keller-Segel system; blow-up of solutions; existence; stability
Summary: Some structures of the solution set for an elliptic boundary value problem describing the stationary state of the Keller-Segel system are presented. First, we control the blow-up of solutions. Then, some facts on existence and non-existence of the solution are proven. We also study the linearized stability. These theorems provide us with an expected bifurcation diagram for the disc region. This result is richer than that conjectured through numerical computation in the early 1980s, and explains the reason for the discrepancy between the conjecture on the non-stationary Keller-Segel system at that time and a recently proven theorem.