traveling waves of some symmetric planar flows of non-newtonian fluids

We present some variants of burgers-type equations for incompressible and isothermal planar flow of viscous non-newtonian fluids based on the cross, the carreau and the power-law rheology models, and on a symmetry assumption on the flow. we numerically solve the associated traveling wave equations by using industrial data and in order to validate the models we prove existence and uniqueness of solutions to the equations. we also provide numerical estimates of the shock thickness as well as the maximum stress associated with the traveling waves.