Electron. J. Differential Equations, Vol. 2017 (2017), No. 23, pp. 1-16.

On a reaction-diffusion system associated with brain lactate kinetics

Remy Guillevin, Alain Miranville, Angelique Perrillat-Mercerot

Abstract:
Our aim in this article is to study properties of a reaction-diffusion system which is related with brain lactate kinetics, when spatial diffusion is taken into account. In particular, we prove the existence and uniqueness of nonnegative solutions and obtain linear stability results. We also derive $L^\infty $-bounds on the solutions. These results give insights on the therapeutic management of glioma.

Submitted November 18, 2016. Published January 18, 2017.
Math Subject Classifications: 35K57, 35K67, 35B45.
Key Words: Brain lactate kinetics; spatial diffusion; reaction-diffusion system; well-posedness; regularity; linear stability.

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Rémy Guillevin
Université de Poitiers
F-86962 Chasseneuil Futuroscope Cedex, France
email: remy.guillevin@chu-poitiers.fr
Alain Miranville
Université de Poitiers
F-86962 Chasseneuil Futuroscope Cedex, France
email: alain.miranville@math.univ-poitiers.fr
Angélique Perrillat-Mercerot
Université de Poitiers
F-86962 Chasseneuil Futuroscope Cedex, France
email: Angelique.Perrillat@math.univ-poitiers.fr

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