论文标题
出租车消费系统中的界限，涉及信号依赖性运动以及密度确定的扩散和交叉扩散的同时增强
Boundedness in a taxis-consumption system involving signal-dependent motilities and concurrent enhancement of density-determined diffusion and cross-diffusion
论文作者
论文摘要
本文涉及涉及信号依赖性动力的迁移消费式出租车系统$ \ weft \ weft \ {arben {array} {l} u_t =Δ \ qquad \ qquad \ qquad（\ star）$$在平滑边界域中$ω\ subset \ mathbb {r}^n $，其中$ m> 1 $和$ n \ ge2 $。 It is shown that if $ϕ\in C^3([0,\infty))$ is strictly positive on $[0,\infty)$, for all suitably regular initial data an associated no-flux type initial-boundary value problem possesses a globally defined bounded weak solution, provided $m>\frac{n}{2}$, which is consistent with the restriction imposed on $m$ in corresponding signal production counterparts of $（\ star）$以建立类似的结果。
This paper is concerned with the migration-consumption taxis system involving signal-dependent motilities $$\left\{ \begin{array}{l} u_t = Δ\big(u^mϕ(v)\big), \\[1mm] v_t = Δv-uv, \end{array} \right. \qquad \qquad (\star)$$ in smoothly bounded domains $Ω\subset\mathbb{R}^n$, where $m>1$ and $n\ge2$. It is shown that if $ϕ\in C^3([0,\infty))$ is strictly positive on $[0,\infty)$, for all suitably regular initial data an associated no-flux type initial-boundary value problem possesses a globally defined bounded weak solution, provided $m>\frac{n}{2}$, which is consistent with the restriction imposed on $m$ in corresponding signal production counterparts of $(\star)$ so as to establish the similar result.
