Springer
Inverse Obstacle Scattering with Non-Over-Determined Scattering Data
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The inverse obstacle scattering problem consists of finding the unknown surface of a body (obstacle) from the scattering ����(����;����;����), where ����(����;����;����) is the scattering amplitude, ����;���� ���� ����2 is the direction of the scattered, incident wave, respectively, ����2 is the unit sphere in the R3 and k > 0 is the modulus of the wave vector. The scattering data is called non-over-determined if its dimensionality is the same as the one of the unknown object. By the dimensionality one understands the minimal number of variables of a function describing the data or an object. In an inverse obstacle scattering problem this number is 2, and an example of non-over-determined data is ����(����) := ����(����;����0;����0). By sub-index 0 a fixed value of a variable is denoted. It is proved in this book that the data ����(����), known for all ���� in an open subset of ����2, determines uniquely the surface ���� and the boundary condition on ����. This condition can be the Dirichlet, or the Neumann, or the impedance type. The above uniqueness theorem is of principal importance because the non-over-determined data are the minimal data determining uniquely the unknown ����. There were no such results in the literature, therefore the need for this book arose. This book contains a self-contained proof of the existence and uniqueness of the scattering solution for rough surfaces.
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- Springer
- EAN / GTIN
- 9783031024184