Fixed energy inverse scattering for noncompactly supported potentials
โ Scribed by A.G. Ramm; P.D. Stefanov
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 553 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0895-7177
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let[V2 + k2n(x~,23)]u(x1,x2,x3) = -6(x1 -y1)6(x2 -y2)6(~3 -ys) in R"+. Assume that U(XI,X~,X~ = 0, yl,y2 = 0, y3 = 0, k) is measured at the plane P := {x : 23 = 0) for all positions of the source on the line y = (yi, y2 = 0, ys = 0), -oo < yr < 00, and receiver on the plane (~1, x2, x3 = 0), -oo < x
## A new inversion formula is obtained for the 3D inverse scattering problem with fixedenergy exact data (IP). A new stability estimate and an inversion formula are obtained for the above problem with noisy, fixed-energy data. An algorithm is described for solving IP.
Let A q (ฮฑ , ฮฑ, k) be the scattering amplitude, corresponding to a local potential q(x), x โ R 3 , q(x) = 0 for |x| > a, where a > 0 is an arbitrary large fixed number, ฮฑ , ฮฑ โ S 2 are unit vectors, S 2 is the unit sphere in R 3 , ฮฑ is the direction of the incident wave, k 2 > 0 is the energy. We pr
Let q ( x ) be. a real-valued function with compact support D c R3. Given the scattering amplitude A(a', a, k) for all a', a E S 2 and a fixed frequency k > 0, the moments of q(x) up to the second order are found using a computationally simple and relatively stable two-step procedure. First, one fin