Abstract
Our aim in this paper is to study properties of a parabolic-elliptic system related with brain lactate kinetics. These equations are obtained from a reaction-diffusion system, when a small parameter vanishes. In particular, we prove the existence and uniqueness of nonnegative solutions and obtain error estimates on the difference of the solutions to the initial reaction-diffusion system and those to the limit one, on bounded time intervals. We also study the linear stability of the unique spatially homogeneous equilibrium.
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Acknowledgements
This paper is dedicated to Gianni Gilardi, with friendship and admiration. The author wishes to thank an anonymous referee for her/his careful reading of the paper and useful comments.
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Miranville, A. (2017). Mathematical Analysis of a Parabolic-Elliptic Model for Brain Lactate Kinetics. In: Colli, P., Favini, A., Rocca, E., Schimperna, G., Sprekels, J. (eds) Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs. Springer INdAM Series, vol 22. Springer, Cham. https://doi.org/10.1007/978-3-319-64489-9_15
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DOI: https://doi.org/10.1007/978-3-319-64489-9_15
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