论文标题
在更高维度的抛物线抛物线凯勒 - 塞格系统的大型全球解决方案
Large global solutions of the parabolic-parabolic Keller-Segel system in higher dimensions
论文作者
论文摘要
我们研究了抛物线抛物线凯勒 - 塞格系统在$ \ r^d，d \ ge 2 $中的全球存在。我们证明，只要扩散参数$τ$在趋化因子的方程中足够大，任意大小的初始数据就会产生全局解决方案。在Biler，Guerra \＆Karch（2015）和Corrias，Escobedo \＆Matos（2014）之前，在二维案例中观察到了这一事实。我们的分析改善了早期的结果，并将其扩展到任何维度$ d \ ge 3 $。 Our size conditions on the initial data for the global existence of solutions seem to be optimal, up to a logarithmic factor in $τ$, when $τ>>1$: we illustrate this fact by introducing two toy models, both consisting of systems of two parabolic equations, obtained after a slight modification of the nonlinearity of the usual Keller-Segel system.对于这些玩具模型，我们在同伴论文[4]中建立了一类大型解决方案的有限时间爆炸。
We study the global existence of the parabolic-parabolic Keller-Segel system in $\R^d , d \ge 2$. We prove that initial data of arbitrary size give rise to global solutions provided the diffusion parameter $τ$ is large enough in the equation for the chemoattractant. This fact was observed before in the two-dimensional case by Biler, Guerra \& Karch (2015) and Corrias, Escobedo \& Matos (2014). Our analysis improves earlier results and extends them to any dimension $d \ge 3$. Our size conditions on the initial data for the global existence of solutions seem to be optimal, up to a logarithmic factor in $τ$, when $τ>>1$: we illustrate this fact by introducing two toy models, both consisting of systems of two parabolic equations, obtained after a slight modification of the nonlinearity of the usual Keller-Segel system. For these toy models, we establish in a companion paper [4] finite time blowup for a class of large solutions.
