DIRICHLET PROBLEM OF POISSON EQUATIONS ON A TYPE OF HIGHER-DIMENSIONAL FRACTAL SETS

Le Zhu, Yipeng Wu, Zhilong Chen, Kui Yao, Shuai Huang and Yuan Wang
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Le Zhu: Army Engineering University of PLA, Nanjing 211101, P. R. China
Yipeng Wu: Army Engineering University of PLA, Nanjing 211101, P. R. China†Institute of Defense Engineering, AMS, PLA, Wuhan 430019, P. R. China
Zhilong Chen: Army Engineering University of PLA, Nanjing 211101, P. R. China
Kui Yao: Army Engineering University of PLA, Nanjing 211101, P. R. China
Shuai Huang: ��Institute of Defense Engineering, AMS, PLA, Wuhan 430019, P. R. China
Yuan Wang: ��Institute of Defense Engineering, AMS, PLA, Wuhan 430019, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 03, 1-8

Abstract: Poisson equation is a partial differential equation with broad utility in theoretical physics. Dirichlet problem of Poisson Equations can be solved by Green’s function. It is a very attractive problem to look for analogous results of the above problem in the fractal context. This paper studies the network set Higher-Dimensional Sierpinski Gaskets, solves Dirichlet problem of Poisson Equations on them by expressing Green’s function explicitly.

Keywords: Higher-Dimensional Networks; Poisson Equations; Laplace Operator; Self-Similar Sets (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22500517

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