Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Mathematical study of a nonlinear neuron multi-dendritic model

Author: Pierluigi Colli
Journal: Quart. Appl. Math. 52 (1994), 689-706
MSC: Primary 92C20; Secondary 35K60, 35Q80
DOI: https://doi.org/10.1090/qam/1306044
MathSciNet review: MR1306044
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Abstract: A mathematical model of potential spreading along neuron dendrites is proposed to describe the synaptic transmissions in the so-called cerebellar granule cells, which consist of a nearly spherical soma emitting a finite number of dendrites. The model accounts for the nonlinear dependence of the NMDA receptors, located at the virtual ends of any dendrite, upon the voltage. The corresponding initial-boundary value problem is formulated in the framework of Sobolev spaces. Existence and uniqueness of a weak solution are proved along with regularity results ensuring that the solution is classical.

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Additional Information

DOI: https://doi.org/10.1090/qam/1306044
Article copyright: © Copyright 1994 American Mathematical Society

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