Analysis of a mathematical model for brain lactate kinetics
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 differe...
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| Format: | Article |
| Language: | English |
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AIMS Press
2018-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2018056 |
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| _version_ | 1832590048209403904 |
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| author | Carole Guillevin Rémy Guillevin Alain Miranville Angélique Perrillat-Mercerot |
| author_facet | Carole Guillevin Rémy Guillevin Alain Miranville Angélique Perrillat-Mercerot |
| author_sort | Carole Guillevin |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5a21562a2f8940c3aa8f8fbd5585313f |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2018-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-5a21562a2f8940c3aa8f8fbd5585313f2025-01-24T02:41:02ZengAIMS PressMathematical Biosciences and Engineering1551-00182018-09-011551225124210.3934/mbe.2018056Analysis of a mathematical model for brain lactate kineticsCarole Guillevin0Rémy Guillevin1Alain Miranville2Angélique Perrillat-Mercerot3Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 7348, Equipe DACTIM-MIS, CHU de Poitiers, 2 Rue de la Milétrie, F-86021 Poitiers, FranceUniversité de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 7348, Equipe DACTIM-MIS, CHU de Poitiers, 2 Rue de la Milétrie, F-86021 Poitiers, FranceUniversité 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, FranceUniversité 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, FranceThe 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.https://www.aimspress.com/article/doi/10.3934/mbe.2018056brain lactate kineticsfast-slow systemregularitywell-posednesslinear stabilitylimit systemsimulationsin vivo data |
| spellingShingle | Carole Guillevin Rémy Guillevin Alain Miranville Angélique Perrillat-Mercerot Analysis of a mathematical model for brain lactate kinetics Mathematical Biosciences and Engineering brain lactate kinetics fast-slow system regularity well-posedness linear stability limit system simulations in vivo data |
| title | Analysis of a mathematical model for brain lactate kinetics |
| title_full | Analysis of a mathematical model for brain lactate kinetics |
| title_fullStr | Analysis of a mathematical model for brain lactate kinetics |
| title_full_unstemmed | Analysis of a mathematical model for brain lactate kinetics |
| title_short | Analysis of a mathematical model for brain lactate kinetics |
| title_sort | analysis of a mathematical model for brain lactate kinetics |
| topic | brain lactate kinetics fast-slow system regularity well-posedness linear stability limit system simulations in vivo data |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2018056 |
| work_keys_str_mv | AT caroleguillevin analysisofamathematicalmodelforbrainlactatekinetics AT remyguillevin analysisofamathematicalmodelforbrainlactatekinetics AT alainmiranville analysisofamathematicalmodelforbrainlactatekinetics AT angeliqueperrillatmercerot analysisofamathematicalmodelforbrainlactatekinetics |