We study a parabolic system of chemotaxis introduced by E. F. Keller and L. A. Segel. First, norm behaviors of the blow-up solution are proven. Then some kind of symmetry breaking and the concentration toward the boundary follow when the $L^1$ norm of the initial value is less than 8$pi$. Meanwhile a method of rearrangement is proposed to prove an inequality of Trudinger-Moser's type.
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机译：我们研究了由E. F. Keller和L. A. Segel引入的趋化性抛物线系统。首先，证明了爆破解决方案的规范行为。然后，当初始值的$ L ^ 1 $范数小于8 $ pi $时，就会发生某种对称性破坏和向边界的集中。同时，提出了一种重排方法来证明Trudinger-Moser型不等式。
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