论文标题
描述趋化大肠杆菌菌落的双曲线 - 纤维素 - 羟基助PDE模型
A hyperbolic-elliptic-parabolic PDE model describing chemotactic E. coli colonies
论文作者
论文摘要
我们研究了描述细菌\ textit {escherichia coli}菌落模式的形成的初始有限值问题的修改版本。在数值和分析上研究了三个抛物线方程的原始系统，并洞悉了趋化性的潜在机制。我们在这里专注于抛物线 - 纤维素 - 抛物线近似值和双曲线 - 纤维素 - 抛物线限制系统，该系统描述了纯趋化运动而没有随机扩散的情况。我们首先为抛物线 - 涡轮抛物线系统构建局部解决方案。然后，我们证明了统一的\ textit {a先验}估计值，并将它们与紧凑的参数一起使用，以构建用于双曲线 - elliptic-Parabolic限制系统的局部时间解决方案。最后，我们证明某些初始条件会产生解决方案，这些解决方案在所有空间维度中在$ l^\ infty $ norm中的有限时间爆炸。即使在空间维度1中，紫罗兰色也是真实的，对于完整的抛物线或抛物线式Keller-Segel系统而言，情况并非如此。
We study a modified version of an initial-boundary value problem describing the formation of colony patterns of bacteria \textit{Escherichia Coli}. The original system of three parabolic equations was studied numerically and analytically and gave insights into the underlying mechanisms of chemotaxis. We focus here on the parabolic-elliptic-parabolic approximation and the hyperbolic-elliptic-parabolic limiting system which describes the case of pure chemotactic movement without random diffusion. We first construct local-in-time solutions for the parabolic-elliptic-parabolic system. Then we prove uniform \textit{a priori} estimates and we use them along with a compactness argument in order to construct local-in-time solutions for the hyperbolic-elliptic-parabolic limiting system. Finally, we prove that some initial conditions give rise to solutions which blow-up in finite time in the $L^\infty$ norm in all space dimensions. This last result violet is true even in space dimension 1, which is not the case for the full parabolic or parabolic-elliptic Keller-Segel systems.
