| Abstract: |
| From sonars to medical imaging or even robot vacuum cleaners, acoustic scattering is at the core of numerous applications.
In an acoustic scattering problem, an incident acoustic field is scattered by an obstacle in such a way that the total field -- superposition of the incident and scattered ones -- satisfies a given boundary condition.
Modelling that problem, a crucial aspect is the geometry of the obstacle, and it is known that irregular shapes such as fractals are most relevant to represent the behaviour of real-life objects.
In this talk, we discuss the acoustic scattering problem by an obstacle described by a Sobolev extension domain.
Those domains can be smooth, Lipschitz, but also fractal, multi-fractal...
That obstacle is endowed with an impedance-type boundary condition, understood with but also without a boundary measure.
Relying on tools from potential theory, we study the well-posedness of the impedance scattering problem in both cases, which we restate in terms of boundary equations.
As an application of our analysis, we consider the inverse scattering problem consisting in identifying the obstacle and the boundary condition from many scattered plane waves. |
|