Uncertain partial differential equation with application to heat conduction |
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| Authors: | Xiangfeng Yang Kai Yao |
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| Institution: | 1.School of Information Technology and Management,University of International Business and Economics,Beijing,China;2.Department of Mathematical Sciences,Tsinghua University,Beijing,China;3.School of Economics and Management,University of Chinese Academy of Sciences,Beijing,China |
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| Abstract: | This paper first presents a tool of uncertain partial differential equation, which is a type of partial differential equations driven by Liu processes. As an application of uncertain partial differential equation, uncertain heat equation whose noise of heat source is described by Liu process is investigated. Moreover, the analytic solution of uncertain heat equation is derived and the inverse uncertainty distribution of solution is explored. This paper also presents a paradox of stochastic heat equation. |
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