Inverse Obstacle Scattering with Non-Over-Determined Scattering Data

By Alexander G. Ramm

The inverse obstacle scattering problem consists of finding the unknown surface of a body (obstacle) from the scattering ����(����;����;����), where ����(����;����;����) is the scattering amplitude, ����;���� ���� ���� is the direction of the scattered, incident wave, respectively, ���� 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 ���� , 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.

• Format: Paperback
• Language: English
• ISBN: 3031012909
• ISBN13: 9783031012907
• Release Date: June 2019
• Publisher: Springer
• Length: 53 Pages
• Weight: 0.31 lbs.
• Dimensions: 0.1" x 7.5" x 9.3"