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arXiv · 2406.11746

Location of blow-up points in fully parabolic chemotaxis systems with spatially heterogeneous logistic source

Mario Fuest·Johannes Lankeit·Masaaki Mizukami
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Abstract

We consider the fully parabolic, spatially heterogeneous chemotaxis-growth system \begin{align*} \begin{cases} u_t = \Delta u - \nabla\cdot(u\nabla v) + \kappa(x)u-\mu(x)u^2, \\ v_t = \Delta v - v + u \end{cases} \end{align*} in bounded domains $\Omega\subset \mathbb{R}^2$ and show that the blow-up set is contained in the set of zeroes of $\mu$.

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Mario Fuest, Johannes Lankeit, Masaaki Mizukami. 2024-06-17. Location of blow-up points in fully parabolic chemotaxis systems with spatially heterogeneous logistic source. https://doi.org/10.3934/dcds.2024148

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