The inverse problem for a general class of multidimensional hyperbolic equations
type: Item
instance of: scholarly article
title: The inverse problem for a general class of multidimensional hyperbolic equations
zbMATH Open document ID: 1264.35277
DOI: 10.1155/2012/891078
author: Gani Aldashev
author: S. A. Aldashev
published in: Mathematical Problems in Engineering
publication date: 2013-06-11T00:00:00Z
review text: Summary: Inverse problems for hyperbolic equations are found in geophysical prospecting and seismology, and their multidimensional analogues are especially important for applied work. However, whereas results have been established for the some narrow classes of hyperbolic equations, no results exist for more general classes. This paper proves the solvability of the inverse problem for a general class of multidimensional hyperbolic equations. Our approach consists of properly choosing the shape of the overidentifying condition that is needed to determine the right-hand side of the hyperbolic PDE and then applying the Fourier series method. We are then able to establish the results of the existence of solution for the cases when the unknown right-hand side is time- independent or space independent.
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35L20
zbMATH DE Number: 6173670
Wikidata QID: Q58912617
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/891078
OpenAlex ID: W2076158346
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description: scientific article; zbMATH DE number 6173670