Abstract:

We considered the mathematical model of scattering problem for time harmonic acoustic waves in anisotropic media above an unbounded sound soft rough surface. We gave a variational form of the problem and established the infsup condition of the sesquilinear form. By means of a Rellichlike identity and the generalized LaxMilgram theorem, we proved that the variational problem is uniquely solvable for arbitrary wave number and we also gave a priori estimation. These results are available for more general media besides isotropic ones.

Key words: scattering problem, Helmholtz equation, rough surface