{"product_id":"inverse-obstacle-scattering-with-non-over-determined-scattering-data-von-alexander-g-ramm","title":"Inverse Obstacle Scattering with Non-Over-Determined Scattering Data","description":"\n                                \n                \u003cp\u003eThe inverse obstacle scattering problem consists of finding the unknown surface of a body (obstacle) from the scattering ����(����;����;����), where ����(����;����;����) is the scattering amplitude, ����;���� ���� ����² is the direction of the scattered, incident wave, respectively, ����² is the unit sphere in the ℝ³ and k \u0026gt; 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.\u003c\/p\u003e\n                                \n                \n                \u003cp\u003eIt is proved in this book that the data ����(����), known for all ���� in an open subset of ����², determines uniquely the surface ���� and the boundary condition on ����. This condition can be the Dirichlet, or the Neumann, or the impedance type.\u003c\/p\u003e\n                                \n                \n                \u003cp\u003eThe 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.\u003c\/p\u003e\n                            \n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783031012907\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783031012907","offer_id":40175573532765,"sku":"9783031012907","price":29.95,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/1bb16771-bead-4a07-98e2-3dfefe0cb17e.jpg?v=1775621055","url":"https:\/\/shop.autorenwelt.de\/en\/products\/inverse-obstacle-scattering-with-non-over-determined-scattering-data-von-alexander-g-ramm","provider":"Autorenwelt Shop","version":"1.0","type":"link"}