Asymptotics of the mild solution of awave equation in three-dimensional space driven by a general stochastic measure

Bodnarchuk, I. M. (2019). Asymptotics of the mild solution of awave equation in three-dimensional space driven by a general stochastic measure. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics(4), 12–17. https://doi.org/10.17721/1812-5409.2019/4.2

We study the Cauchy problem for a wave equation in three-dimensional space driven by a general stochastic measure. Under some assumptions, we prove that the mild solution tends to zero almost surely as the absolute value of the spatial variable tends to infinity.Key words: asymptotic behavior, stochastic measure, stochastic wave equation, mild solution, Besov space.Pages of the article in the issue: 12 - 17Language of the article: English