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This work is devoted to the study of migraine with aura in the human brain. Following
[6], we class migraine as a propagation of a wave of depolarization through
the cells. The mathematical model used, based on a reaction-diffusion equation, is briefly
presented. The equation is considered in a duct containing a bend, in order to model one
of the numerous circumvolutions of the brain. For a wide set of parameters, one can
establish the existence...
We consider the radiative transfer equation (RTE) with reflection in a three-dimensional
domain, infinite in two dimensions, and prove an existence result. Then, we study the
inverse problem of retrieving the optical parameters from boundary measurements, with help
of existing results by Choulli and Stefanov. This theoretical analysis is the framework of
an attempt to model the color of the skin. For this purpose, a code has been developed to
solve...
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