期刊
INVERSE PROBLEMS
卷 22, 期 3, 页码 923-938出版社
IOP PUBLISHING LTD
DOI: 10.1088/0266-5611/22/3/012
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Suppose n > 1 is an odd integer, f is a smooth function supported in a ball B with boundary S, and u is the solution of the initial value problem utt - Delta(x)u = 0, (x,t) is an element of R-n x [0,infinity); u(x, t = 0) = 0, u(t)(x,t = 0) = f (x), x is an element of R-n. We characterize the range of the map f -> u\S x[0,infinity) and give a stable scheme for the inversion of this map. This also characterizes the range of the map sending f to its mean values over spheres centred on S.
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