Ramm Alexander G. Inverse Obstacle Scattering with Non-Over-Determined Scattering Data 9781681735887

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Автор: Ramm Alexander G.
Название: Inverse Obstacle Scattering with Non-Over-Determined Scattering Data
ISBN: 9781681735887
Издательство: Mare Nostrum (Eurospan)
Классификация:

Основы высшей математики и математический анализ

Вычислительная математика

Математическое и статистическое ПО

Теория вычислительных машин и систем, кибернетика

ISBN-10: 1681735881
Обложка/Формат: Paperback
Страницы: 69
Вес: 0.14 кг.
Дата издания: 30.05.2019
Серия: Synthesis lectures on mathematics and statistics
Язык: English
Размер: 235 x 191 x 4
Читательская аудитория: Professional and scholarly
Ключевые слова: Computer science,Mathematical & statistical software,Calculus & mathematical analysis,Numerical analysis, COMPUTERS / Computer Science,MATHEMATICS / Numerical Analysis,COMPUTERS / Mathematical & Statistical Software
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Поставляется из: Англии
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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.

Inverse Obstacle Scattering with Non-Over-Determined Scattering Data, Ramm Alexander G.