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

Abstract

This paper is concerned with a three-component chemotaxis model accounting for indirect signal production,reading as $u_t=\nabla \cdot (\nabla u-u\nabla v)$,$v_t=\Delta v-v+w$ and $0=\Delta w-w+u$,posed in a ball of ${\mathbb{R}}^n$ with $n\ge 5$,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 $(u_0,v_0)\in C^0(\overline{\Omega })\times C^2(\overline{\Omega })$ with ${\int }_{\Omega }{u}_0=m$ such that the corresponding solutions blow up in finite time.

References in corpus (4)

• New critical exponents in a fully parabolic quasilinear Keller-Segel and applications to volume filling models
• Finite-time blow-up in fully parabolic quasilinear Keller-Segel systems with supercritical exponents
• Singular limit of a chemotaxis model with indirect signal production and phenotype switching
• Global solvability and unboundedness in a fully parabolic quasilinear chemotaxis model with indirect signal production