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Analysis of a mathematical model for brain lactate kinetics

1. Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 7348, Equipe DACTIM-MIS, CHU de Poitiers, 2 Rue de la Milétrie, F-86021 Poitiers, France
2. Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 7348, Equipe DACTIM-MIS, Boulevard Marie et Pierre Curie - Téléport 2, F-86962 Chasseneuil Futuroscope Cedex, France

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The aim of this article is to study the well-posedness and properties of a fast-slow system which is related with brain lactate kinetics. In particular, we prove the existence and uniqueness of nonnegative solutions and obtain linear stability results. We also give numerical simulations with different values of the small parameter $\varepsilon$ and compare them with experimental data.

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