Singular limit problem for the two-dimensional Keller-Segel system in scaling critical space
Singular limit problem for the two-dimensional Keller-Segel system in scaling critical space
复制标题
DOI：
10.1016/j.jde.2020.06.012
复制
发表时间：
2020-11
影响因子：
2.4
通讯作者：
Masaki Kurokiba;T. Ogawa
中科院分区：
文献类型：
--
作者：
Masaki Kurokiba;T. Ogawa
在二维临界空间中考虑Keller-Segel方程柯西问题的奇异极限问题。证明了Keller-Segel系统在标度临界函数空间的解作为松弛时间参数τ→∞强收敛于临界空间中抛物-椭圆型方程(简化的Keller-Segel方程)的漂移扩散组的解。作为证明，我们证明了热方程的广义极大正则性，并系统地利用它与插补空间B·Q，σS(R2)和F·Q，σS(R2)之间的嵌入序列来证明奇异极限问题。
We consider the singular limit problem of the Cauchy problem to the Keller-Segel equation in the two dimensional critical space. It is shown that the solution to the Keller-Segel system in the scaling critical function space converges to the solution to the drift-diffusion system of parabolic-elliptic equations (the simplified Keller-Segel equation) in the critical space strongly as the relaxation time parameter τ→∞. For the proof, we show generalized maximal regularity for the heat equations and use it systematically with the sequence of embeddings between the interpolation spaces B˙ q, σ s (R 2) and F˙ q, σ s (R 2) for the proof of singular limit problem.