Electron. J. Differential Equations, Vol. 2025 (2025), No. 98, pp. 1-21.

Blow-up prevention and rate of convergence of solutions for N-dimensional parabolic-parabolic systems with consumption of chemoattractant

Jiashan Zheng, Yuying Wang

Abstract:
This article studies the Neumann-boundary initial-value problem for a parabolic-parabolic chemotaxis-consumption system in a smooth bounded domain. For regular nonnegative initial data, we prove that the classical solution to the corresponding no-flux problem remains globally and uniformly bounded under structural assumptions. This is achieved through a novel trigonometric-type weight function rather than an exponential one; therefore we not only significantly improve previous results, but also providing a versatile context to resolve pertinent systems. More importantly, we confirm the convergence of the solution to an equilibrium constant.

Submitted August 4, 2025. Published October 16, 2025.
Math Subject Classifications: 35K20, 35K55, 92C17.
Key Words: Chemotaxis; blow-up prevention; chemoattractant consumption; global existence; exponential decay.
DOI: 10.58997/ejde.2025.98

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Jiashan Zheng
School of Mathematics and Information Sciences
Yantai University, Yantai 264005, China
email: zhengjiashan2008@163.com
Yuying Wang
School of Mathematics and Information Sciences
Yantai University, Yantai 264005, China
email: wangyuy2024@163.com

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