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On uncertain partial differential equations

Author

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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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