The inverse obstacle scattering problem consists of finding the unknown surface of a body (obstacle) from the scattering A(B;a;k), where A(B;a;k) is the scattering amplitude, B;a E S2 is the direction of the scattered, incident wave, respectively, S2 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 A(B) := A(B;a0;k0). By sub-index 0 a fixed value of a variable is denoted.
It is proved in this book that the data A(B), known for all B in an open subset of S2, determines uniquely the surface S and the boundary condition on S. 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 S. 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.
- ISBN10 168173589X
- ISBN13 9781681735894
- Publish Date 12 June 2019
- Publish Status Temporarily Withdrawn
- Publish Country US
- Imprint Morgan & Claypool
- Format eBook
- Pages 69
- Language English