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DOI码：10.1007/s40304-016-0091-4

发表刊物：Communications in Mathematics and Statistics

关键字：Inverse problem; Stability; Carleman estimate; Hyperbolic equation

摘要：For the solution to ∂^2_t u(x, t)−Δu(x, t)+q(x)u(x, t) = δ(x, t) and u |_{t<0}=0, consider an inverse problem of determining q(x), x ∈Ω from data f = u |_{S_T} and g = (∂u/∂n) |_{S_T} . Here Ω⊂{(x_1, x_2, x_3) ∈ R^3 | x_1 > 0} is a bounded domain, S_T = {(x, t) | x ∈ ∂Ω, |x| < t < T + |x|}, n = n(x) is the outward unit normal n to ∂Ω, and T > 0. For suitable T > 0, prove a Lipschitz stability estimation: ||q_1 − q_2||_{L^2(Ω)} ≤ C{||f_1 − f_2||_{H^1(S_T) }+ ||g_1 − g_2||_{L^2(S_T)}}, provided that q1 satisfies a priori uniform boundedness conditions and q2 satisfies a priori uniform smallness conditions, where uk is the solution to problem (1.1) with q = q_k , k = 1, 2.

合写作者：李书敏

第一作者：秦雪

论文类型：期刊论文

学科门类：理学

文献类型：J

卷号：4

期号：3

页面范围：403-421

ISSN号：2194-6701

是否译文：否

发表时间：2016-09-12

发布期刊链接：https://link.springer.com/article/10.1007/s40304-016-0091-4