Geodesic
Two-point boundary problem for string oscillation equationwith given velocity in arbitrary point of time.~I
Trudy Instituta matematiki, Tome 18 (2010) no. 2, pp. 22-35

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Boundary value problem in a half-hand for the equation of string vibration with given velocity at any time of string vibration is considered. An analytic solution for the considered problem is built. 
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     author = {V. I. Korzyuk and I. S. Kozlovskaya},
     title = {Two-point boundary problem for string oscillation equationwith given velocity in arbitrary point of {time.~I}},
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V. I. Korzyuk; I. S. Kozlovskaya. Two-point boundary problem for string oscillation equationwith given velocity in arbitrary point of time.~I. Trudy Instituta matematiki, Tome 18 (2010) no. 2, pp. 22-35. http://geodesic.mathdoc.fr/item/TIMB_2010_18_2_a2/