论文标题
凯勒 - 塞格类型的抛物线系统的尖锐适应性和爆炸结果
Sharp well-posedness and blowup results for parabolic systems of the Keller-Segel type
论文作者
论文摘要
我们研究了在对通常双抛物线凯勒 - 塞格系统的非线性进行稍作修改后获得的两个玩具模型。对于这些玩具模型，包括由两个抛物线方程组成的系统，我们确定在适当意义上的数据中，该数据比化学吸引剂方程中的扩散参数$τ$要小，我们获得了全球解决方案，以及对于某些大于$τ$的数据，是有限的时间爆炸。这样，我们检查了全球存在的大小条件对于大$τ$，最多是对数因素。
We study two toy models obtained after a slight modification of the nonlinearity of the usual doubly parabolic Keller-Segel system. For these toy models, both consisting of a system of two parabolic equations, we establish that for data which are, in a suitable sense, smaller than the diffusion parameter $τ$ in the equation for the chemoattractant, we obtain global solutions, and for some data larger than $τ$ , a finite time blowup. In this way, we check that our size condition for the global existence is sharp for large $τ$ , up to a logarithmic factor.
