Global Boundedness in a Quasilinear Chemotaxis-consumption System With Signal-dependent Motility and Super-quadratic Damping
Year: 2025
Type: article
Abstract: In this paper, we consider a quasilinear chemotaxis-consumption model $ \left\{ \begin{array}{lll} u_t=\Delta (v^{\alpha}u^{m})+ru-\mu u^{l},\quad &x\in\Omega,\; t>0,\\ v_t=\Delta v-uv, &x\in\Omega,\; t>0 \end{array} \right. $ within a smoothly bounded domain $ \Omega\subset\mathbb{R}^n $ under homogeneous Neumann boundary conditions, where the parameters $ \alpha, r, \mu>0 $ and $ l, m>1 $. For any sufficiently regular initial data and parameters $ l, m>1 $ with $ l>m+1 $, it is shown that the aforementioned system possesses at least one global weak solution with a boundedness property $ \|u(\cdot,t)\|_{L^{p}(\Omega)}+\|v(\cdot,t)\|_{W^{1,\infty}(\Omega)}\leq C $ for all $ p\geq 2 $ and $ t>0 $. This finding indicates the regularizing effect of super-quadratic damping of a logistic-type source under strong degeneracy of signal-dependent motility, even though the cross-diffusion is simultaneously enhanced.
DOI: 10.11948/20240271
Author: Chi Xu
Institution: Anhui University of Science and Technology
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4411533742