Geodesic
Solvability of the inverse problem of external influence in the many-dimensional wave equation
Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 13 (2011), pp. 27-37

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The solvability of the inverse problem of finding a solution problem $u(x,t)$ and the unknown coefficients $q_{1}(t),\ldots,q_{m}(t)$ in the many-dimensional hyperbolic equation when setting the conditions for initial boundary value problem and the conditions of the overdetermination. Existence of solutions are proven.
Keywords: inverse problem, conditions of redefinition, hyperbolic equation, wave equation, a priori estimate. 
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     author = {S. S. Pavlov},
     title = {Solvability of the inverse problem of external influence in the many-dimensional wave equation},
     journal = {Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika},
     pages = {27--37},
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     number = {13},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VCHGU_2011_13_a2/}
}
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S. S. Pavlov. Solvability of the inverse problem of external influence in the many-dimensional wave equation. Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 13 (2011), pp. 27-37. http://geodesic.mathdoc.fr/item/VCHGU_2011_13_a2/