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- W4295113564 abstract "Abstract We consider the singular limit problem for the Cauchy problem of the (Patlak–) Keller–Segel system of parabolic-parabolic type. The problem is considered in the uniformly local Lebesgue spaces and the singular limit problem as the relaxation parameter $$tau $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>τ</mml:mi> </mml:math> goes to infinity, the solution to the Keller–Segel equation converges to a solution to the drift-diffusion system in the strong uniformly local topology. For the proof, we follow the former result due to Kurokiba–Ogawa [20–22] and we establish maximal regularity for the heat equation over the uniformly local Lebesgue and Morrey spaces which are non-UMD Banach spaces and apply it for the strong convergence of the singular limit problem in the scaling critical local spaces." @default.
- W4295113564 created "2022-09-10" @default.
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- W4295113564 date "2022-09-10" @default.
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- W4295113564 title "Maximal regularity of the heat evolution equation on spatial local spaces and application to a singular limit problem of the Keller–Segel system" @default.
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- W4295113564 doi "https://doi.org/10.1007/s00208-022-02469-7" @default.
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