An inverse random source problem for the Helium production-diffusion equation driven by a fractional Brownian motion
Numerical Analysis
2022-06-07 v1 Numerical Analysis
Abstract
In this paper, we consider the prediction of the helium concentrations as function of a spatially variable source term perturbed by fractional Brownian motion. For the direct problem, we show that it is well-posed and has a unique mild solution under some conditions. For the inverse problem, the uniqueness and the instability are given. In the meanwhile, we determine the statistical properties of the source from the expectation and covariance of the final-time data u(r,T). Finally, numerical implements are given to verify the effectiveness of the proposed reconstruction.
Keywords
Cite
@article{arxiv.2206.02359,
title = {An inverse random source problem for the Helium production-diffusion equation driven by a fractional Brownian motion},
author = {Jing Li and Hao Cheng and Xiaoxiao Geng},
journal= {arXiv preprint arXiv:2206.02359},
year = {2022}
}
Comments
arXiv admin note: text overlap with arXiv:2101.04744 by other authors