On a reaction-diffusion system associated with brain lactate kinetics

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.

Keywords

• Brain lactate kinetics
• spatial diffusion
• reaction-diffusion system
• well-posedness
• regularity
• linear stability