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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

Justification of the Fourier method for hyperbolic equations with random initial conditions


Authors: Yu. V. Kozachenko and G. I. Slivka
Translated by: Oleg Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 69 (2003).
Journal: Theor. Probability and Math. Statist. 69 (2004), 67-83
MSC (2000): Primary 60G35; Secondary 35L20
Published electronically: February 8, 2005
MathSciNet review: 2110906
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Abstract | References | Similar Articles | Additional Information

Abstract: Conditions for the existence of a twice differentiable solution of a hyperbolic type partial differential equation with random strongly $\operatorname{Sub}_{\varphi}(\Omega)$ initial conditions are found in the multidimensional case.


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Additional Information

Yu. V. Kozachenko
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, Kyiv National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: yvk@univ.kiev.ua

G. I. Slivka
Affiliation: Department of Mathematical Analysis, Faculty for Mathematics, Uzhgorod University, Pidgirna Street 46, Uzhgorod, Ukraine
Email: aslyvka@yahoo.com

DOI: http://dx.doi.org/10.1090/S0094-9000-05-00615-0
PII: S 0094-9000(05)00615-0
Received by editor(s): March 28, 2003
Published electronically: February 8, 2005
Article copyright: © Copyright 2005 American Mathematical Society