{ "item_title" : "Inverse Obstacle Scattering with Non-Over-Determined Scattering Data", "item_author" : [" Alexander G. Ramm "], "item_description" : "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.", "item_img_path" : "https://covers4.booksamillion.com/covers/bam/3/03/101/290/3031012909_b.jpg", "price_data" : { "retail_price" : "29.99", "online_price" : "29.99", "our_price" : "29.99", "club_price" : "29.99", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

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