The mixed Dirichlet-Neumann-Cauchy problem for second order hyperbolic operators (Q1359569)

The author investigates a hyperbolic mixed initial boundary-value problem in which the Neumann condition and the Dirichlet condition are given on complementary parts of boundary. He obtains an existence and uniqueness result in Sobolev spaces with additional differentiation in the tangential directions to the interface by deriving energy estimates and applying a duality argument. Moreover, the author analyzes the asymptotic behavior of the solutions near the interface by the Wiener-Hopf method.