Thesis Summary:

In this work we consider a mixture formed by a viscous fluid and particulate material dispersed in it formed mainly by small solid particles of different species and different sizes. The model that emerges from combining a Shallow Water (or Saint Venant) system with a polydispersed sedimentation system, this allows to know both the vertical behavior of the species in the mixture as well as the horizontal movement of them in the fluid. The multilayer model appears after dividing the domain along the vertical direction into $M$ layers of size $h_alpha$, resulting in a multilayered Shallow Water model with polydispersed sedimentation in two horizontal dimensions, which can be written as a hyperbolic system With non-homogeneous non-conservative products.