Abstract
Seepage equation in fissured porous media is a partial differential equation describing the variation of pressure of a given area over time. In traditional seepage equation, the strength of mass source is supposed to be deterministic. However, the mass source in practice is often affected by noise such as transformation of underground environment and geological activities. To depict the noise, some scholars attempted to employ a technique called Winner process. Unfortunately, it is unreasonable to model the noise in seepage equation with Winner process, since change rate of pressure will be infinite. As a alternative tool in uncertainty theory, Liu process is introduced to model the noise, which can refrain from the problem of infinity. Then this paper deduces the uncertain seepage equation in fissured porous media driven by Liu process. Furthermore, the analytic solution and its inverse uncertainty distribution are derived. Finally, a paradox of stochastic seepage equation in fissured porous media is presented.
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Acknowledgements
This work was supported by the Scientific Research Program of Shaanxi Provincial Department of Education No. 20JK0149, Key Projects of National Statistical Science Research No. 2021LZ28, the Yanta Scholars Fund of Xi’an University of Finance and Economics, Xi’an University of Finance and Economics Young Talent Support Program, and the National Natural Science Foundation of China Grant No. 61873329.
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Yang, L., Ye, T. & Yang, H. Uncertain seepage equation in fissured porous media. Fuzzy Optim Decis Making 21, 383–403 (2022). https://doi.org/10.1007/s10700-021-09370-z
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DOI: https://doi.org/10.1007/s10700-021-09370-z