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arXiv · 2412.10772

Finite-time blowup in a parabolic-parabolic-elliptic chemotaxis model involving indirect signal production

Xuan Mao·Yuxiang Li
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Abstract

This paper is concerned with a three-component chemotaxis model accounting for indirect signal production,reading as $u_t = \nabla\cdot(\nabla u - u\nabla v)$,$v_t = Δv - v + w$ and $0 = Δw - w + u$,posed in a ball of $\mathbb R^n$ with $n\geq5$,subject to homogeneous Neumann boundary conditions.The system is a Nagai-type variant of its fully parabolic version that has a four-dimensional critical mass phenomenon concerning blowup in finite or infinite time according to the seminal works of Fujie and Senba [J. Differential Equations, 263 (2017), 88--148; 266 (2019), 942--976].We prove that for any prescribed mass $m > 0$, there exist radially symmetric and positive initial data $(u_0,v_0)\in C^0(\overlineΩ)\times C^2(\overlineΩ)$ with $\int_Ωu_0 = m$ such that the corresponding solutions blow up in finite time.

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Xuan Mao, Yuxiang Li. 2026-01-05. Finite-time blowup in a parabolic-parabolic-elliptic chemotaxis model involving indirect signal production. https://doi.org/10.1007/s00245-025-10287-x

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