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2010•Journal of the Indian Mathematical SocietyRequires access

A Mathematical Model of Microbial Growth in a Chemostat

Padma Murali, Rajiv Kumar

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Abstract

In this paper, a new mathematical model of bacterial culture in a chemostat is studied and analyzed. We study a general nonlinear age dependent population dynamics model which is a generalization of the chemostat model and obtain the existence, uniqueness, the semigroup property and the continuous dependence of the solutions on the initial data for the general model. Then, we show that the chemostat model is a particular case of the general model and hence conclude the wellposedness of the chemostat model.

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What this paper is about

In this paper, a new mathematical model of bacterial culture in a chemostat is studied and analyzed. We study a general nonlinear age dependent population dynamics model which is a generalization of the chemostat model and obtain the existence, uniqueness, the semigroup property and the continuous dependence of the solutions on the initial data for the general model. Then, we show that the chemostat model is a particular case of the general model and hence conclude the wellposedness of the chemostat model.

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Available abstract

In this paper, a new mathematical model of bacterial culture in a chemostat is studied and analyzed. We study a general nonlinear age dependent population dynamics model which is a generalization of the chemostat model and obtain the existence, uniqueness, the semigroup property and the continuous dependence of the solutions on the initial data for the general model. Then, we show that the chemostat model is a particular case of the general model and hence conclude the wellposedness of the chemostat model.

Key concepts: Chemostat, Mathematics, Uniqueness, Generalization, Applied mathematics, Property (philosophy), Semigroup, Population

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