Bingham fluid in a thin layer

Consider a nonlinear model that describes the behavior of a Bingham fluid in a thin layer represented by the open] 0, 1 [×] ε > 0, is a small parameter. After transforming the problem into a problem defined on open sets ] 0, 1 [×] 0, 1 [, we study the limit when ε→0. We study the existence and uniqueness of the problem limit and compared with a one-dimensional model used by engineers