On a singular mathematical model for brain lactate kinetics

Abstract

In this paper, we consider a singular nonlinear differential system that characterizes the intricate dynamics of brain lactate kinetics between cells and capillaries, as described by System (1.1) below. We begin by establishing the existence and uniqueness of nonnegative solutions for our system through the application of Schauder's fixed‐point theorem. Subsequently, we explore the behavior of these solutions as the viscosity term approaches zero, shedding light on the system's dynamic evolution in such scenarios. To provide empirical validation for our theoretical findings, we offer a series of numerical simulations. These simulations not only confirm the results we have obtained but also reinforce prior research, underscoring the model's efficiency in capturing the complexities of the brain's lactate kinetics. Our work contributes not only to the theoretical underpinning of this field but also to its practical implications, making it a valuable resource for both researchers and practitioners seeking to comprehend and manipulate these vital biological processes.