| Abstract: |
| We consider a no-flux initial-boundary value problem for the degenerate volume-filling chemotaxis system with diffusion and chemotactic sensitivity depending on cell densities and signal concentration. We first prove that there exists a global weak solution. Second, under some additional conditions, we show uniqueness of global weak solutions with the mass conservation law. Moreover, we construct a flat-hump-shaped stationary solution in the one-dimensional setting. These results extend the ones in Laurencot-Wrzosek (2005), where they studied a related problem with diffusion and chemotactic sensitivity depending only on cell densities. |
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