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Dear authors! Submission of all materials is carried out only electronically through Online Submission System in personal account. DOI: 10.46698/s030119598380s Recovery of Rapidly Oscillated RightHand Side of the Wave Equation by the Partial Asymptotics of the Solution
Abstract:
The initialboundary problem for the onedimensional wave equation with unknown rapidly oscillated righthandside is considered in the paper. The latter is represented as a product of two functions; the first function depends on the spatial variable and the second one depends on time and fast time variables. Four different cases are considered: in two cases one of the factorfunctions is known and in two other cases both factorfunctions are unknown. In each of these cases, the inverse problems of recovering unknown functions from some information about partial asymptotics of the original problem with known data are posed and solved. This specified information consists, in general, in setting values for certain asymptotics coefficients in some spatial and/or time points. The use of some additional conditions (overdetermination conditions) in this form speaks of a fundamental difference between the above statements of inverse problems and the classics, where additional conditions are imposed on exact solutions. The construction of solutions asymptotics of the original problem with this approach act as direct problem. This approach to inverse problems with rapidly oscillated data in time is developed by the author over the past few years.
Keywords: onedimensional wave equation, rapidly oscillating absolute term, asymptotics of solution, inverse problem
Language: Russian
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For citation: Babich, P. V. and Levenshtam, V. B. Recovery of Rapidly Oscillated RightHand Side of the Wave Equation by the Partial Asymptotics of the Solution, Vladikavkaz Math. J., 2020, vol. 22, no. 4, pp.2844 (in Russian). DOI 10.46698/s030119598380s ← Contents of issue 
 

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