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Uncertain seepage equation in fissured porous media

Author

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  • Lu Yang

    (Xi’an University of Finance and Economics)

  • Tingqing Ye

    (Tsinghua University)

  • Haizhong Yang

    (Xi’an University of Finance and Economics)

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.

Suggested Citation

  • Lu Yang & Tingqing Ye & Haizhong Yang, 2022. "Uncertain seepage equation in fissured porous media," Fuzzy Optimization and Decision Making, Springer, vol. 21(3), pages 383-403, September.
    • Handle: RePEc:spr:fuzodm:v:21:y:2022:i:3:d:10.1007_s10700-021-09370-z
    DOI: 10.1007/s10700-021-09370-z
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    References listed on IDEAS

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    1. Yang, Xiangfeng, 2018. "Solving uncertain heat equation via numerical method," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 92-104.
    2. Kai Yao & Baoding Liu, 2020. "Parameter estimation in uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 1-12, March.
    3. Yang, Xiangfeng & Liu, Yuhan & Park, Gyei-Kark, 2020. "Parameter estimation of uncertain differential equation with application to financial market," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    4. Xiangfeng Yang & Kai Yao, 2017. "Uncertain partial differential equation with application to heat conduction," Fuzzy Optimization and Decision Making, Springer, vol. 16(3), pages 379-403, September.
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