On uncertain partial differential equations

被引：4

作者：

Zhu, Yuanguo ^{[1
]}

机构：

[1] Nanjing Univ Sci & Technol, Sch Math & Stat, Nanjing 210094, Peoples R China

来源：

FUZZY OPTIMIZATION AND DECISION MAKING | 2024年 / 23卷 / 02期

关键词：

Uncertain differential equations; Liu process; Partial differential equation; Uncertainty distribution; Heat conduction equation; STABILITY;

D O I：

10.1007/s10700-023-09418-2

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

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-path method is introduced to obtain the inverse uncertainty distributions of solutions to UPDEs.

引用

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页码：219 / 237

页数：19

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