Acoustic wave scattering by inhomogeneous obstacles in layered media

Acoustic Scattering by Inhomogeneous Obstacles

Acoustic scattering problems are considered when the material parameters (density and speed of sound) are functions of position within a bounded region. An integro-differential equation for the pressure in this region is obtained. It is proved that solving this equation is equivalent to solving the scattering problem. Problems of this kind are often solved by regarding the effects of the inhomo...

Acoustic scattering by inhomogeneous spheres.

Acoustic scattering problems are considered when the material parameters (density rho and speed of sound c) are spherically symmetric functions of position. Explicit separated solutions are derived (i) when rho(r) = exp(beta r) and c(-2) is a linear function of r(-1), and (ii) when rho(r) = exp(-beta r2) and c(-2) is a linear function of r2. In both cases, the radial parts of the solutions are ...

Scattering by Obstacles in Acoustic Waveguides

We study the scattering of acoustic waves by an obstacle embedded in a uniform waveguide with planar boundaries, which is a fundamental model in shallow ocean acoustics. Under certain geometric assumptions on the shape of the obstacle, we prove a Rellichtype uniqueness theorem in the case of soft obstacles. The solvability of the scattering problem is proved via boundary integral equations and ...

Spherically symmetric inhomogeneous bianisotropic media: Wave propagation and light scattering

Transmission Eigenvalues for Inhomogeneous Media Containing Obstacles

We consider the interior transmission problem corresponding to the inverse scattering by an inhomogeneous (possibly anisotropic) media in which an impenetrable obstacle with Dirichlet boundary conditions is embedded. Our main focus is to understand the associated eigenvalue problem, more specifically to prove that the transmission eigenvalues form a discrete set and show that they exist. The pr...