Stability of the inverse problem in potential scattering at fixed energy
نویسندگان
چکیده
منابع مشابه
Inverse scattering problem with fixed energy and fixed incident direction
Let A q (α ′ , α, k) be the scattering amplitude, corresponding to a local potential q(x), x ∈ R 3 , q(x) = 0 for |x| > a, where a > 0 is a fixed number, α ′ , α ∈ S 2 are unit vectors, S 2 is the unit sphere in R 3 , α is the direction of the incident wave, k 2 > 0 is the energy. We prove that given an arbitrary function f (α ′) ∈ L 2 (S 2), an arbitrary fixed α 0 ∈ S 2 , an arbitrary fixed k ...
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Let IA,(B’B) A(@’, @)I < 6, where 6 > 0 is a small given number, A(@’ , 8 ) is the unknown scattering amplitude at a fixed k > 0 corresponding to a potential q(x)EL2(Bu), q(x) = q(x), q(x) = 0 in a,:= R’\B,, Bo:= {x: 1x1 < a } , @ ‘ , B E S 2 , the unit sphere. Functions qa(x) are constructed, given S z 0 and the function A,(@’ ,@) , such that 11% q/IL2(B,) 4 0 as 6 4 0. The function A,(B’, 0) ...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 1990
ISSN: 0373-0956
DOI: 10.5802/aif.1239