Non-uniqueness in an Overdetermined Cauchy Problem for the Wave Equation

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J. Math. Sci. Univ. Tokyo
Vol. 9 (2002), No. 3, Page 545--563.

Takiguchi, Takashi
Non-uniqueness in an Overdetermined Cauchy Problem for the Wave Equation
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Abstract:
In this paper, we prove non-uniqueness in an overdetermined Cauchy problem for the wave equation in quasi-analytic ultradistribution category. In our Cauchy problem we give initial values at one space point. It is an inverse problem to reconstruct the wave from observation at one space point.

Mathematics Subject Classification (2000): Primary 35L05; Secondary 35N99, 34K29

Mathematical Reviews Number: MR1930418

Received: 2002-02-14

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