Analysis of a mathematical model for brain lactate kinetics

Carole Guillevin; Rémy Guillevin; Alain Miranville; Angélique Perrillat-Mercerot; Carole Guillevin; Rémy Guillevin; Alain Miranville; Angélique Perrillat-Mercerot

doi:10.3934/mbe.2018056

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 5: 1225-1242. doi: 10.3934/mbe.2018056

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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

Received: 20 October 2017 Revised: 27 January 2018 Published: 01 October 2018
MSC : 34A34, 35B09, 35Q92

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.
- Brain lactate kinetics,
- fast-slow system,
- regularity,
- well-posedness,
- linear stability,
- limit system,
- simulations,
- in vivo data
Citation: Carole Guillevin, Rémy Guillevin, Alain Miranville, Angélique Perrillat-Mercerot. Analysis of a mathematical model for brain lactate kinetics[J]. Mathematical Biosciences and Engineering, 2018, 15(5): 1225-1242. doi: 10.3934/mbe.2018056

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Abstract

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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