Well-Posedness and Regularity of Solutions to Neural Field Problems with Dendritic Processing
Daniele Avitabile,
Nikolai V. Chemetov,
P. M. Lima
Abstract:We study solutions to a recently proposed neural field model in which dendrites are modelled as a continuum of vertical fibres stemming from a somatic layer. Since voltage propagates along the dendritic direction via a cable equation with nonlocal sources, the model features an anisotropic diffusion operator, as well as an integral term for synaptic coupling. The corresponding Cauchy problem is thus markedly different from classical neural field equations. We prove that the weak formulation of the problem admi… Show more
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