This paper is concerned with blowup in a parabolic-parabolic system describing chemotactic aggregation. In a disk, radial solutions blow up in finite time if their initial energy is less than some value. In the whole plane, the energy diverges to −∞ as time goes to +∞ for any forward selfsimilar solution. This implies that one cannot expect to get a sufficient condition for finite-time blowup using energy as in a disk. For a solution $(u,v)$, u and v denote density of cells and of chemical substance, respectively. Let τ be the coefficient of time derivative of v. We first prove that for $\tau >0$ there exists $M(\tau )>0$ with $M(\tau )\to \infty$ as $\tau \to \infty$ such that all radial solutions $(u,v)$ with initial mass of u larger than $M(\tau )$ blow up in finite time. On the other hand, it was shown in [22] that any blowup in the system with $\tau =1$ is type II (not necessarily in radial case). Removing the restriction on τ, we get the conclusion for all $\tau >0$.

本文与抛物线-抛物线系统中描述化学趋向聚集的爆炸有关。在磁盘中，如果径向解的初始能量小于某个值，则会在有限的时间内爆炸。在整个平面中，对于任何正向自相似解，随着时间流逝至+∞，能量的偏差变为-∞。这意味着不能期望像磁盘一样使用能量来获得有限时间爆燃的充分条件。寻找解决方案$（ü，v）$，ü和v分别表示细胞的密度化学物质，分别的和。设τ为v的时间导数。我们首先证明$\tau >0$ 那里存在 $\mathrm{中号}（\tau ）>0$ 与 $\mathrm{中号}（\tau ）\to \infty$ 如 $\tau \to \infty$ 这样所有径向解 $（ü，v）$u的初始质量大于$\mathrm{中号}（\tau ）$在有限的时间内爆炸。另一方面，在[22]中表明，系统中的任何爆炸$\tau =\mathrm{1个}$是II型（在径向情况下不一定）。消除对τ的限制，我们可以得出所有结论$\tau >0$。