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Inverse Obstacle Scattering with Non-Over-Determined Scattering Data, Hardback Book

Inverse Obstacle Scattering with Non-Over-Determined Scattering Data Hardback

Part of the Synthesis Lectures on Mathematics and Statistics series


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.


  • Format: Hardback
  • Pages: 69 pages
  • Publisher: Morgan & Claypool Publishers
  • Publication Date:
  • Category: Numerical analysis
  • ISBN: 9781681735900

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