论文标题
与间接信号产生和非统治对称情况的趋化系统中啤酒密度的出现
Emergence of lager densities in chemotaxis system with indirect signal production and non-radial symmetry case
论文作者
论文摘要
本文介绍了以下趋化系统的经典解决方案，并具有广义的逻辑增长和间接信号产生\ begin {eqnarray} \ left \ weak {\ begin {array} {llll}＆u_t =amΔuu-\ nabla \ nabla \ cdot \ cdot（u \ nabla v） 0 =d_1ΔV-βV+αw，\\＆0 =d_2ΔW-δW+γu\ end {array} \ right。 \ qquad（0.1）\ end {eqnArray}和所谓的强$ w^{1，q}（ω）$ - 双曲线 - elliptic- elliptic模型的解决方案\ begin {eqnarray} \ weft \ left \ left \ left \ left \ webt { v）+ru-μu^θ，\\＆0 =d_1ΔV-βV+αw，\\＆0 =d_2Δw-Δw-Δw+γu，\ end {array} \ right。 $ n \ geq1 $，其中$ r，μ，d_1，d_2，α，β，γ，δ> 0 $和$θ> 1 $。通过应用粘度消失的方法，我们首先证明（0.1）的经典解决方案将收敛到强$ W^{1，q}（ω）$ - （0.2）的解决方案为$ε\ rightArrow0 $。在构造了（0.2）的本地井井之后，我们发现强$ w^{1，q}（ω）$ - 解决方案将在有限的时间内爆炸，如果$ω$是一个有界的凸面域，$θ\ in（1，2] $，则在（如果添加一个正常的$ m）（如果添加一个$ M的$ M M），则（如果添加一个$ M）。存在正常常数$ε_0（m）$，$ε\ in（0，\ε_0（m））$，那么（0.1）的经典解决方案在意义上可以超过任意大的有限价值：一个人可以找到一些点$ \ left（\ tilde {x} {x} {x}，\ tilde {tilde {t} \ right） \ tilde {t}）> m $。
This paper deals with the classical solution of the following chemotaxis system with generalized logistic growth and indirect signal production \begin{eqnarray} \left\{ \begin{array}{llll} & u_t=εΔu-\nabla\cdot(u\nabla v)+ru-μu^θ,\\ & 0=d_1Δv-βv+αw,\\ & 0=d_2Δw-δw+γu \end{array} \right. \qquad(0.1)\end{eqnarray} and the so-called strong $W^{1, q}(Ω)$-solution of hyperbolic-elliptic-elliptic model \begin{eqnarray} \left\{ \begin{array}{llll} & u_t=-\nabla\cdot(u\nabla v)+ru-μu^θ,\\ & 0=d_1Δv-βv+αw,\\ & 0=d_2Δw-δw+γu, \end{array} \right.\ \qquad(0.2)\end{eqnarray} in arbitrary bounded domain $Ω\subset\mathbb{R}^n$, $n\geq1$, where $r, μ, d_1, d_2, α, β, γ, δ>0$ and $θ>1$. Via applying the viscosity vanishing method, we first prove that the classical solution of (0.1) will converge to the strong $W^{1, q}(Ω)$-solution of (0.2) as $ε\rightarrow0$. After structuring the local well-pose of (0.2), we find that the strong $W^{1, q}(Ω)$-solution will blow up in finite time with non-radial symmetry setting if $Ω$ is a bounded convex domain, $θ\in(1, 2]$, and the initial data is suitable large. Moreover, for any positive constant $M$ and the classical solution of (0.1), if we add another hypothesis that there exists positive constant $ε_0(M)$ with $ε\in(0,\ ε_0(M))$, then the classical solution of (0.1) can exceed arbitrarily large finite value in the sense: one can find some points $\left(\tilde{x}, \tilde{t}\right)$ such that $u(\tilde{x}, \tilde{t})>M$.
