Inverse Obstacle Scattering with Non-Over-Determined Scattering Data
暫譯: 非過度確定散射數據的逆障礙散射
Ramm, Alexander G., Krantz, Steven G.
- 出版商: Morgan & Claypool
- 出版日期: 2019-06-12
- 售價: $1,450
- 貴賓價: 9.5 折 $1,378
- 語言: 英文
- 頁數: 69
- 裝訂: Quality Paper - also called trade paper
- ISBN: 1681735881
- ISBN-13: 9781681735887
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商品描述
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.
商品描述(中文翻譯)
反向障礙散射問題的目標是從散射數據中找出物體(障礙物)的未知表面,其中散射數據為 (;;),而 (;;) 是散射幅度;分別為散射波和入射波的方向, 是在 ℝ3 中的單位球,且 k > 0 是波向量的模。
散射數據稱為非過度確定(non-over-determined),如果其維度與未知物體的維度相同。這裡的維度是指描述數據或物體的函數所需的最小變數數量。在反向障礙散射問題中,這個數量為 2,而非過度確定數據的一個例子是 (): = (;₀;₀)。下標 0 表示變數的固定值。
本書證明了在開子集中的所有數據 () 唯一地確定了表面及其邊界條件。這個條件可以是 Dirichlet 邊界條件、Neumann 邊界條件或阻抗類型的邊界條件。
上述唯一性定理具有重要意義,因為非過度確定數據是唯一確定未知數的最小數據。在文獻中並沒有這樣的結果,因此本書的需求應運而生。本書包含了對粗糙表面散射解的存在性和唯一性的自足證明。