English

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

Analysis of PDEs 2025-04-11 v1

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 ΩR2\Omega\subset \mathbb{R}^2 and show that the blow-up set is contained in the set of zeroes of μ\mu.

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Cite

@article{arxiv.2406.11746,
  title  = {Location of blow-up points in fully parabolic chemotaxis systems with spatially heterogeneous logistic source},
  author = {Mario Fuest and Johannes Lankeit and Masaaki Mizukami},
  journal= {arXiv preprint arXiv:2406.11746},
  year   = {2025}
}

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16 pages