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On uncertain partial differential equations

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  • Yuanguo Zhu

    (Nanjing University of Science and Technology)

Abstract

Uncertain partial differential equation (UPDE) was introduced in literature. But the solution of a UPDE was not defined well. In this article, we will rigorously give a suitable concept of a UPDE and define its solution by an integral equation. Then, some examples are given to show the rationality of the definition. Uncertain heat conduction equation is presented as an application of UPDE. For those UPDEs having no analytic solutions, $$\alpha$$ α -path method is introduced to obtain the inverse uncertainty distributions of solutions to UPDEs.

Suggested Citation

  • Yuanguo Zhu, 2024. "On uncertain partial differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 23(2), pages 219-237, June.
    • Handle: RePEc:spr:fuzodm:v:23:y:2024:i:2:d:10.1007_s10700-023-09418-2
    DOI: 10.1007/s10700-023-09418-2
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    References listed on IDEAS

    as
    1. Yang Liu & Baoding Liu, 2022. "Residual analysis and parameter estimation of uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 21(4), pages 513-530, December.
    2. Tingqing Ye & Baoding Liu, 2023. "Uncertain hypothesis test for uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 22(2), pages 195-211, June.
    3. Xiangfeng Yang & Hua Ke, 2023. "Uncertain interest rate model for Shanghai interbank offered rate and pricing of American swaption," Fuzzy Optimization and Decision Making, Springer, vol. 22(3), pages 447-462, September.
    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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    Cited by:

    1. Lu Yang & Yang Liu, 2025. "Numerical solution of uncertain partial differential equations and its applications," Fuzzy Optimization and Decision Making, Springer, vol. 24(1), pages 69-98, March.

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