Abstract
It is shown that in a certain wave equation the coefficient is uniquely determined if the Cauchy data are given and if the solution of the equation is known as a function on a plane and of time.
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S. L. Sobolev, Some Applications of Functional Analysis to Mathematical Physics [in Russian], LGU, Leningrad (1950).
V. I. Smirnov, Course in Higher Mathematics [in Russian], Vol. 4, Nauka, Moscow (1974).
Yu. E. Anikonov, “On the uniqueness of the solution of integral equations of the first kind,” Matem. Zametki,14, No. 4, 493–498 (1973).
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Translated from Matematicheskie Zametki, Vol. 19, No. 2, pp. 211–214, February, 1976.
The author would like to thank V. G. Romanov for helpful remarks.
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Anikonov, Y.E. A uniqueness theorem for solutions to an inverse problem for the wave equation. Mathematical Notes of the Academy of Sciences of the USSR 19, 127–128 (1976). https://doi.org/10.1007/BF01098744
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DOI: https://doi.org/10.1007/BF01098744