| Abstract: |
| We introduce the Keller-Segel model for describing the aggregation phenomenon
of certain microorganisms called slime molds, which have a characteristic property
called chemotaxis. Chemotaxis is the motion toward higher concentration of a chemical substance. This kind of microorganism, when put in a nutrition-poor environment, produces a chemical substance that attracts other individuals within the same population. This leads to the formation of an aggregation which produces spores. In this way, the slime molds propagate next generation. From mathematical point of view, the aggregation phenomenon can be interpreted as the blow-up of the solution two simultaneous partial differential equations. In this talk, we show that the blow-up solution never exists if the mass of the slime molds is less than a certain value. |
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