Wave equation for a homogeneous string with fixed ends driven by a stable random noise

Rusanyuk, L.; Shevchenko, G.

doi:10.1090/tpms/1069

Wave equation for a homogeneous string with fixed ends driven by a stable random noise

Authors: L. I. Rusanyuk and G. M. Shevchenko
Translated by: N. N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 98 (2018).
Journal: Theor. Probability and Math. Statist. 98 (2019), 171-181
MSC (2010): Primary 60H15, 35L05; Secondary 35R60, 60G52
DOI: https://doi.org/10.1090/tpms/1069
Published electronically: August 19, 2019
MathSciNet review: 3824685
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Abstract: A wave equation with external forces is considered in this paper for a homogeneous string with fixed ends. The distribution of the right-hand side of the equation is symmetric $\alpha$ -stable. It is proved that the function constructed by the Fourier method is a generalized solution of the equation. The regularity of the trajectories is also established.

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