Abstract

AbstractThe paper is devoted to the development of the theory of inverse problems for evolution equations with terms rapidly oscillating in time. A new approach to setting such problems is developed for the case in which additional constraints are imposed only on several first terms of the asymptotics of the solution rather than on the whole solution. This approach is realized in the case of a multidimensional hyperbolic equation with unknown absolute term.KeywordsMultidimensional hyperbolic equationRapidly oscillating absolute termAsymptotics of solutionInverse problemMathematics Subject ClassificationPrimary 35B4035R30; Secondary 35L1035L15

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