Seminar on Qualitative Theory of Differential Equations - Masaki Kurokiba (11.10.2018)
Thursday 11.10.2018 at 15:00, Lecture room M/223
By: Pavol Quittner
Masaki Kurokiba (Muroran Institute of Technology):
Singular limit problem for the Keller-Segel system to a drift-diffusion system in critical spaces
We consider the singular limit problem of the Cauchy problem for the Keller-Segel problem in the critical function spaces. It is shown that the solution to the Keller-Segel system in the scaling critical function spaces converges to the solution to the drift-diffusion system of parabolic-elliptic equations (simplified Keller-Segel model) in the critical space strongly as a relaxation time parameter goes to infinity. For the proof, we employ generalized maximal regularity for heat equations and use it systematically with the sequence of embeddings between the interpolation spaces.