An inverse problem with data on the part of the boundary
نویسنده
چکیده
Let ut = $ u q(x)u :1⁄4 Lu in D · [0,1), where D R is a bounded domain with a smooth connected boundary S, and q(x) 2 L(S) is a real-valued function with compact support in D. Assume that u(x, 0) = 0, u = 0 on S1 S, u = a(s, t) on S2 = SnS1, where a(s, t) = 0 for t > T, a(s, t) 6 0, a 2 C([0,T];H(S2)) is arbitrary. Given the extra data uN jS2 1⁄4 bðs; tÞ, for each a 2 C ([0,T];H(S2)), where N is the outer normal to S, one can find q(x) uniquely. A similar result is obtained for the heat equation ut 1⁄4 Lu :1⁄4 r ðaruÞ. These results are based on new versions of Property C. 2006 Elsevier B.V. All rights reserved.
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