On the rigid-lid approximation of shallow water Bingham

This paper discusses the well posedness of an initial value problem describing motion a Bingham fluid in basin with degenerate bottom topography. A physical interpretation such is discussed. The system governing obtained from Shallow Water-Bingham models regime where Froude number degenerates, i.e taking limit equations as tends to zero. Since we are considering coefficients, then shall work weighted Sobolev spaces order establish existence weak solution. In overcome difficulty discontinuity Bingham's constitutive law, follow similar approach that introduced [G. DUVAUT and J.-L. LIONS, Springer-Verlag, 1976]. We study also behavior this solution when yield vanishes. Finally, numerical scheme for 1D furnished.