Dongxiu Wang, Anmin Mao, Solutions of an attraction-repulsion chemotaxis system with singular sensitivities

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DOI: 10.23952/jnva.10.2026.5.08

Volume 10, Issue 5, 1 October 2026, Pages 1013-1031

Abstract. This paper investigates the following chemotaxis system $u_{t}=\Delta u-\chi_{1}\nabla\cdot(\frac{u}{v}\nabla v)+\chi_{2}\nabla\cdot(\frac{u}{w}\nabla w)+\lambda u-\mu u^{2}, x\in\Omega,t>0,$
$\tau v_{t}=\Delta v-v+u, x\in\Omega,t>0,$
$0=\Delta w -w+u,x\in\Omega,t>0,$

under homogeneous Neumann boundary conditions, where $\tau\in\{0,1\}$ . In the case of $w\not\equiv0$ , namely, singular attraction-repulsion mechanism, we prove the global boundedness of global classical solution to the system. For $\tau=1$ , if the parameters satisfy $\chi_1\chi_2\in(0,\frac{1}{2})$ , $\chi_2\in(0,\frac{2}{9})$ , and $\lambda$ is sufficiently large, the system admits a unique global uniformly bounded solution. For $\tau=0$ , the system admits a unique global uniformly bounded solution with $\chi_{1}\in(0,\frac{1}{2})$ , which also indicates that no blow-up of solutions occurs over time. We complete our proof by using heat semigroup estimates, a priori estimates, parabolic-elliptic regularity theory, and the Moser iteration technique.

How to Cite this Article:
D. Wang, A. Mao, Solutions of an attraction-repulsion chemotaxis system with singular sensitivities, J. Nonlinear Var. Anal. 10 (2026), 1013-1031.