| Autor: |
Benoît Perthame |
| Jazyk: |
angličtina |
| Rok vydání: |
2011 |
| Předmět: |
|
| Zdroj: |
Journal of the Egyptian Mathematical Society, Vol 19, Iss 1, Pp 52-56 (2011) |
| Druh dokumentu: |
article |
| ISSN: |
1110-256X |
| DOI: |
10.1016/j.joems.2011.09.005 |
| Popis: |
Various classes of Partial Differential Equations have shown to be successful in describing the self-organization of bacterial colonies, a topic also sometimes called socio-biology. For instance parabolic systems are standard; the classical Patlak–Keller–Segel system and Mimura’s system are able to explain two elementary processes underlying qualitative behaviors of populations and complex patterns: oriented drift by chemoattraction and colony growth with local nutrient depletion. More recently nonlinear hyperbolic and kinetic models also have been used to describe the phenomena at a smaller scale. We explain here some motivations for ‘microscopic’ descriptions, the mathematical difficulties arising in their analysis and how kinetic models can help in understanding the unity of these descriptions. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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