Continuum approach to mathematical modelling of multispecies biofilms
Continuum approach to mathematical modelling of multispecies biofilms
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DOI：
10.1007/s11587-016-0294-8
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发表时间：
2017-06-01
影响因子：
1.2
通讯作者：
Mattei, M. R.
中科院分区：
文献类型：
--
作者：
D'Acunto, B.;Frunzo, L.;Mattei, M. R.
这项工作提出了一个贡献的数学建模的形成和生长的多物种生物膜的框架内的连续方法，而不是声称是完整的。生物膜的数学模型往往导致考虑非线性偏微分方程的自由边值问题。重点是定性分析，唯一性和存在性的解决方案和他们的主要性质。生物膜的生命过程是一个复杂的生物过程，它包括菌落的形成、生长、微生物从生物膜上附着到液体中的分离等几个阶段。这些过程中的大多数是建模和讨论。此外，工程和生物学应用的兴趣的一些问题被认为是。事实上，我们讨论的自由边值问题，广泛用于废水处理的生物膜反应器，和新的物种入侵到一个已经构成的生物膜与连续的殖民。使用的主要数学方法是特征线法。原来的微分问题转化为积分方程。然后，应用不动点定理。
The work presents a contribution to the mathematical modelling of formation and growth of multispecies biofilms in the framework of continuum approach, without claiming to be complete. Mathematical models for biofilms often lead to consider free boundary value problems for nonlinear PDEs. The emphasis is on the qualitative analysis, uniqueness and existence of solutions and their main properties. Biofilm life is a complex biological process formed by several phases from the formation, development of colonies, attachment and detachment of microbial mass from (to) biofilm to (from) bulk liquid. Most of these processes are modelled and discussed. Moreover, some problems of interest for engineering and biological applications are considered. Indeed, we discuss the free boundary value problem related to biofilm reactors extensively used in wastewater treatment, and the invasion of new species into an already constituted biofilm with the successive colonizations. The main mathematical methodology used is the method of characteristics. The original differential problem is converted to integral equations. Then, the fixed point theorem is applied.