Studying the long time dynamics of fermentation models: production of dry and sweet wine

Abstract

In this talk we will consider two classical mathematical models of wine fermentation. The first model will describe the wine-making process that is used to produce dry wine. The second model will be obtained by introducing a term in the equation of the dynamics of the yeast. Thanks to this change it will be possible to inhibit the fermentation of the sugar and as a consequence a sweet wine will be obtained. We will first prove the existence, uniqueness, positiveness and boundedness of solutions for both models. Then we will pass to analyze the long-time dynamics. For the second model we will also provide estimates for the concentration of ethanol, nitrogen and sugar at the end of the process. Moreover, several numerical simulations will be provided to support the theoretical results.