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portada Inverse Obstacle Scattering with Non-Over-Determined Scattering Data
Type
Physical Book
Author
Publisher
Language
English
Pages
53
Format
Paperback
Dimensions
23.5 x 19.1 x 0.4 cm
Weight
0.14 kg.
ISBN13
9783031012907
Edition No.
1
Categories

Inverse Obstacle Scattering with Non-Over-Determined Scattering Data

Alexander G. Ramm (Author) · Springer · Paperback

Inverse Obstacle Scattering with Non-Over-Determined Scattering Data - Ramm, Alexander G.

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Synopsis "Inverse Obstacle Scattering with Non-Over-Determined Scattering Data"

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.

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