| Abstract: |
| We consider the fully parabolic 1d chemotaxis system with diffusion $1/(1+u)$. We prove that the above mentioned nonlinearity, despite being a natural candidate, is not critical. It means that for such a diffusion any initial condition, independently on the magnitude of mass, generates global-in-time solution. In order to prove our theorem we establish a new Lyapunov-like functional associated to the system. Moreover we will discuss boundedness of solutions. This talk is based on a joint work with Tomasz Cie\`slak. |
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