Inverse scattering problem for the wave equation with time-dependent potential
نویسندگان
چکیده
منابع مشابه
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15 صفحه اولAN INVERSE PROBLEM FOR THE WAVE EQUATION WITH A TIME DEPENDENT COEFFICIENT Rakesh
Let Ω ⊂ R, n ≥ 2, be a bounded domain with smooth boundary. Consider utt −4xu+ q(x, t)u = 0 in Ω× [0, T ] u(x, 0) = 0, ut(x, 0) = 0 if x ∈ Ω u(x, t) = f(x, t) on ∂Ω× [0, T ] We show that if u and f are known on ∂Ω× [0, T ], for all f ∈ C∞ 0 (∂Ω× [0, T ]), then q(x, t) may be reconstructed on C = { (x, t) : x∈Ω, 0 < t < T, x− tω & x+ (T − t)ω 6∈ Ω ∀ ω ∈ R, |ω| = 1 } provided q is known at all po...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1989
ISSN: 0022-247X
DOI: 10.1016/0022-247x(89)90069-3