Wave equation with a stable noise

Wave equation with a stable noise

The three-dimensional wave equation is studied in the paper. The right hand side of the equation has a symmetric \alpha -stable distribution. Two cases are considered, namely the cases where the perturbation is a (1) ``white noise'' and (2) ``colored noise''. It is proved for bot...

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Veröffentlicht in:Theory of probability and mathematical statistics 2018, Vol.96, p.145-157
Hauptverfasser: Pryhara, L. I., Shevchenko, G. M.
Format: Artikel
Sprache:eng
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Zusammenfassung:The three-dimensional wave equation is studied in the paper. The right hand side of the equation has a symmetric \alpha -stable distribution. Two cases are considered, namely the cases where the perturbation is a (1) ``white noise'' and (2) ``colored noise''. It is proved for both cases that a candidate for a solution (a function represented by the Kirchhoff formula) is a generalized solution.
ISSN:0094-9000
1547-7363
DOI:10.1090/tpms/1040