Heat equations defined by a class of fractal measures

Wei Tang Hunan First Normal University Sze-Man Ngai Georgia Southern University and Hunan Normal University

Analysis of PDEs mathscidoc:1809.03001

We set up a framework to study one-dimensional heat equations defined by fractal Laplacians associated with self-similar measures with overlaps. We show that for a class of such self-similar measures, a heat equation can be discretized and the finite element method can be applied to yield a system of linear differential equations. We show that the numerical solutions converge to the actual solution and obtain the rate of convergence. We also study some properties of the solutions of the heat equation.
Fractal; Laplacian; heat equation; self-similar measure with overlaps
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@inproceedings{weiheat,
  title={Heat equations defined by a class of fractal measures},
  author={Wei Tang, and Sze-Man Ngai},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180930061901196112157},
}
Wei Tang, and Sze-Man Ngai. Heat equations defined by a class of fractal measures. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180930061901196112157.
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