Geodesic
Inverse coefficient problem for a quasilinear hyperbolic equation with final overdetermination
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 4, pp. 647-666

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The inverse problem of recovering a solution-dependent coefficient multiplying the lowest derivative in a hyperbolic equation is investigated. As overdetermination is required in the inverse problem, an additional condition is imposed on the solution to the equation with a fixed value of the timelike variable. Global uniqueness and local existence theorems are proved for the solution to the inverse problem. An iterative method is proposed for solving the inverse problem. 
@article{ZVMMF_2006_46_4_a8,
     author = {A. Yu. Shcheglov},
     title = {Inverse coefficient problem for a~quasilinear hyperbolic equation with final overdetermination},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {647--666},
     publisher = {mathdoc},
     volume = {46},
     number = {4},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_4_a8/}
}
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A. Yu. Shcheglov. Inverse coefficient problem for a quasilinear hyperbolic equation with final overdetermination. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 4, pp. 647-666. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_4_a8/