Geodesic
Recovery of a Rapidly Oscillating Absolute Term in the Multidimensional Hyperbolic Equation
Matematičeskie zametki, Tome 104 (2018) no. 4, pp. 505-515

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The paper is devoted to the development of the theory of inverse problems for evolution equations with summands rapidly oscillating in time. A new approach to setting such problems is developed for the case in which additional constraints (overdetermination conditions) are imposed only on several first terms of the asymptotics of the solution rather that on the whole solution. This approach is realized in the case of a multidimensional hyperbolic equation with unknown absolute term.
Keywords: multidimensional hyperbolic equation, rapidly oscillating absolute term, asymptotics of solution, inverse problem. 
@article{MZM_2018_104_4_a1,
     author = {P. V. Babich and V. B. Levenshtam},
     title = {Recovery of a {Rapidly} {Oscillating} {Absolute} {Term} in the {Multidimensional} {Hyperbolic} {Equation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {505--515},
     publisher = {mathdoc},
     volume = {104},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_104_4_a1/}
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P. V. Babich; V. B. Levenshtam. Recovery of a Rapidly Oscillating Absolute Term in the Multidimensional Hyperbolic Equation. Matematičeskie zametki, Tome 104 (2018) no. 4, pp. 505-515. http://geodesic.mathdoc.fr/item/MZM_2018_104_4_a1/