ON A NONHOMOGENEOUS SHALLOW-WATER PROBLEM

We present an existence theorem for a shallow-water problem with a dep th-mean velocity formulation and non-homogeneous boundary conditions e xpressing water entering. A result has been already shown in the case of homogeneous boundary conditions. If we prescribe a non-zero velocit y (or normal velocity) on the boundary, we must also prescribe the wat er elevation on the part of the boundary where the flow enters. With t hese boundary conditions, we obtain a priori estimates that show the p roblem has a solution. We build a sequence of approximated solutions t hat preserves energy and to pass to the limit we use a trace theorem f or the space of L(-1) -functions with L(-1) -divergence.