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Well-posedness of a model equation for neurotransmitter diffusion with reactive boundaries

Abstract

We consider a diffusion equation with reactive boundary conditions. The equation is a model equation for the diffusion of classical neurotransmitters in the tortuous space between cells in the brain. The equation determines the concentration of neurotransmitters such as glutamate and GABA (gamma-aminobutyrate) and the probability for neurotransmitter molecules to be immobilized by binding to protein molecules (receptors and transporters) at the cell boundary (cell membrane). On a regularized problem, we derive a priori estimates. Then, by a compactness argument, we show the existence of solutions. By exploiting the particular structure of the boundary reaction terms, we are able to prove that the solutions are unique and continuous with respect to initial data.

Category

Academic article

Language

English

Author(s)

  • Xavier Raynaud
  • Magne André Nordaas
  • Knut Petter Dæhlin Lehre
  • Niels Christian Danbolt

Affiliation

  • Norwegian University of Science and Technology
  • SINTEF Digital / Mathematics and Cybernetics
  • Simula Research Laboratory
  • University of Oslo

Year

2015

Published in

Mathematical Models and Methods in Applied Sciences

ISSN

0218-2025

Volume

25

Issue

2

Page(s)

195 - 227

View this publication at Cristin