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Session 13. Global existence versus blowup in nonlinear parabolic systems |
Eventual smoothness in a three-dimensional chemotaxis systems with logistic source |
| Johannes Lankeit, Universität Paderborn, Germany |
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We prove existence of weak solutions to the chemotaxis system
\begin{align*}
u_t&=\Delta u - \nabla\cdot (u\nabla v) +\kappa u -\mu u^2\\
v_t&=\Delta v-v+u\nonumber
\end{align*}
under homogeneous Neumann boundary conditions in a smooth bounded convex domain \(\Omega\subset \mathbb{R}^3\), for arbitrary values of \(\mu>0\).
Additionally, we show that, after some time, these solutions become classical solutions, provided that \(\kappa\) is not too large.
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