MATHEMATICAL STUDY OF A NONLINEAR NEURON MULTI-DENDRITIC MODEL

A mathematical model of potential spreading along neuron dendrites is proposed to describe the synaptic transmissions in the so-called cereb ellar granule cells, which consist of a nearly spherical soma emitting a finite number of dendrites. The model accounts for the nonlinear de pendence of the NMDA receptors, located at the virtual ends of any den drite, upon the voltage. The corresponding initial-boundary value prob lem is formulated in the framework of Sobolev spaces. Existence and un iqueness of a weak solution are proved along with regularity results e nsuring that the solution is classical.