The one dimensional shallow water equations with Dirichlet boundary conditions on the velocity
The authors study the one-dimensional shallow water equation for a nonviscous fluid with Dirichlet boundary conditions on the velocity. Approximate solutions are constructed and various a priori estimates are proved. Then, by showing the convergence of the approximate solutions, the local existence of the solution and its uniqueness are proved, i.e., the local in time well-posedness of the problem.
scientific article; zbMATH DE number 5866445