Fractal differential equations on the Sierpiński gasket
type: Item
instance of: scholarly article
title: Fractal differential equations on the Sierpiński gasket
zbMATH Open document ID: 0937.31010
DOI: 10.1007/BF01261610
author: Kyallee Dalrymple
author: Robert S. Strichartz
author: Jade P. Vinson
published in: The Journal of Fourier Analysis and Applications
publication date: 2000-05-30T00:00:00Z
full work available at URL: https://eudml.org/doc/59605
review text: The authors consider the bounded Sierpiński gasket and its approximating prefractal graphs. Using the self-similarity of the fractal and the decimation properties of its Laplacian they derive several exact recursive algorithms to compute harmonic and biharmonic functions as well as Dirichlet eigenfunctions on the graphs and on lines. The proofs are based on well-known decimation properties of harmonic and eigenfunctions. The algorithms are illustrated by 43 pages of graphics and used to prove some theorems on specific features of these functions. Solutions to the heat and wave equation are approximated by finite difference schemes. This results in 7 further pages of graphics and the remarkable observation that there is strong evidence for the wave propagator to have infinite speed.
Mathematics Subject Classification ID: 31C20
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 1310354
zbMATH Keywords: Sierpiński gasket
zbMATH Keywords: exact recursive algorithms
zbMATH Keywords: heat operator
zbMATH Keywords: biharmonic equation
zbMATH Keywords: wave operator
zbMATH Keywords: fractal
zbMATH Keywords: biharmonic functions
zbMATH Keywords: Dirichlet eigenfunctions
reviewed by: Volker Metz
MaRDI profile type: Publication
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OpenAlex ID: W1982766449
description: scientific article; zbMATH DE number 1310354