MATHEMATICAL ANALYSIS OF A PARABOLIC-ELLIPTIC MODEL FOR BRAIN LACTATE KINETICS

Alain Miranville (1)

1 LMA [Poitiers] - Laboratoire de mathématiques et applications [UMR 7348]

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.

Mots clés: Brain lactate kinetics; parabolic-elliptic system; reaction-diffusion system; limit system; nonnegative solutions; well-posedness; error estimates; linear stability

Domaines: Equations aux dérivées partielles [math.AP]

Alain Miranville. MATHEMATICAL ANALYSIS OF A PARABOLIC-ELLIPTIC MODEL FOR BRAIN LACTATE KINETICS. 2017. ⟨hal-01445518⟩