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Global solvability to a singular chemotaxis-consumption model with fast and slow diffusion and logistic source

  • * Corresponding author: Liangwei Wang

    * Corresponding author: Liangwei Wang 
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  • In this paper, we consider the following chemotaxis-consumption model with porous medium diffusion and singular sensitivity

    $ \begin{align*} \left\{ \begin{aligned} &u_{t} = \Delta u^{m}-\chi \mathrm{div}(\frac{u}{v}\nabla v)+\mu u(1-u), \\ &v_{t} = \Delta v-u^{r}v, \end{aligned}\right. \end{align*} $

    in a bounded domain $ \Omega\subset\mathbb R^N $ ($ N\ge 2 $) with zero-flux boundary conditions. It is shown that if $ r<\frac{4}{N+2} $, for arbitrary case of fast diffusion ($ m\le 1 $) and slow diffusion $ (m>1) $, this problem admits a locally bounded global weak solution. It is worth mentioning that there are no smallness restrictions on the initial datum and chemotactic coefficient.

    Mathematics Subject Classification: Primary: 35K55, 35B65.


    \begin{equation} \\ \end{equation}
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