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Zeitschrift für Analysis und ihre Anwendungen

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Volume 33, Issue 4, 2014, pp. 417–428
DOI: 10.4171/ZAA/1519

Published online: 2014-10-15

Blow-Up Profiles for a Semilinear Chemotaxis System Arising in Biology

Rong-Nian Wang[1], Tao Wang[2] and Yong Zhou[3]

(1) Shanghai Normal University, China
(2) Nanchang University, China
(3) Xiangtan University, Xiangtan, Hunan, China

We consider the semilinear coupled system of parabolic-elliptic partial di erential equations arising in chemotaxis involving forcing source of exponential growth type and homogeneous Dirichlet boundary conditions. The local existence and uniqueness of nonnegative classical solutions are proved. Also, a lower bound for the blow-up time if the solution blows up in nite time is derived. Moreover, the exponential decay of the associated energies are also studied. The results we obtained here essentially extend some existing results in this area.

Keywords: Chemotaxis system, classical solution, blow up, decay

Wang Rong-Nian, Wang Tao, Zhou Yong: Blow-Up Profiles for a Semilinear Chemotaxis System Arising in Biology. Z. Anal. Anwend. 33 (2014), 417-428. doi: 10.4171/ZAA/1519