On a terminal value problem for stochastic space‐time fractional wave equations

This work is to investigate terminal value problem for a stochastic time fractional wave equation, driven by a cylindrical Wiener process on a Hilbert space. A representation of the solution is obtained by basing on the terminal value data u(T,x)=φ(x)$$ u\left(T,x\right)=\var...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2023-01, Vol.46 (1), p.1206-1226
Main Authors: Tran Bao, Ngoc, Nane, Erkan, Huy Tuan, Nguyen
Format: Article
Language:English
Subjects:
existence and uniqueness
fractional stochastic wave equation
Hilbert space
Inverse problems
Operators (mathematics)
Regularization
regularization method
Regularization methods
terminal value problem
Wave equations
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Summary:This work is to investigate terminal value problem for a stochastic time fractional wave equation, driven by a cylindrical Wiener process on a Hilbert space. A representation of the solution is obtained by basing on the terminal value data u(T,x)=φ(x)$$ u\left(T,x\right)=\varphi (x) $$ and the spectrum of the fractional Laplacian operator (−Δ)s/2$$ {\left(-\Delta \right)}^{s/2} $$ (in a bounded domain X⊂Rd, 0
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.8573