@Article{EAJAM-12-4,
author = {Zhao, Qian and Liu, Bin},
title = {Boundedness in a Forager-Exploiter Model Accounting for Gradient-Dependent Flux-Limitation},
journal = {East Asian Journal on Applied Mathematics},
year = {2022},
volume = {12},
number = {4},
pages = {848--873},
abstract = {<p style="text-align: justify;">The forager-exploiter model with gradient-dependent flux-limitation $$u_t=\Delta u-\chi\nabla \cdot (uk_f(1+|\nabla w|^2)^{-\frac{\alpha}{2}})\nabla w,$$$$v_t=\Delta v-\xi\nabla \cdot (vk_g(1+|\nabla u|^2)^{-\frac{\beta}{2}})\nabla u,$$$$w_t=\Delta w-(u+v)w-\mu w+r(x,t)$$is considered in smooth bounded domains $Ω ⊂ \mathbb{R}^N,$ $N ≥ 2.$ It is shown that if $α &gt;
(N − 2)/N(N − 1),$ $β &gt; 0,$ then for any nonnegative functions $u_0,$ $v_0,$ $w_0∈ W^{2,∞}(Ω)$ such that $u_0 \not\equiv 0$ and $v_0 \not\equiv 0,$ the problem has a global classical solution $(u, v, w) ∈
(C^0
(\overline{Ω} × [0,∞))\cap C^{2,1}(\overline{Ω} × (0,∞)))^3$.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.291021.140222},
url = {https://global-sci.com/article/82495/boundedness-in-a-forager-exploiter-model-accounting-for-gradient-dependent-flux-limitation}
}