One-dimensional wave equations defined by fractal Laplacians

DOI10.1007/s11854-015-0029-xzbMath1386.35411arXiv1406.0207OpenAlexW3102656953MaRDI QIDQ891353

Sze-Man Ngai, John Fun-Choi Chan, Alexander Teplyaev

Publication date: 17 November 2015

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.0207

zbMATH Keywords

weak solutionwave equationfinite element methoditerated function systemfractal measurefractal Laplacian

Mathematics Subject Classification ID

Wave equation (35L05) Fractals (28A80) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)

Related Items (14)

Spectral decimation of a self-similar version of almost Mathieu-type operators ⋮ Weak convergence and spectrality of infinite convolutions ⋮ Schrödinger equations defined by a class of self-similar measures ⋮ Eigenvalues and eigenfunctions of one-dimensional fractal Laplacians ⋮ Spectrality of Moran-Sierpinski type measures ⋮ Strong damping wave equations defined by a class of self-similar measures with overlaps ⋮ Wave equation on one-dimensional fractals with spectral decimation and the complex dynamics of polynomials ⋮ Singularly continuous spectrum of a self-similar Laplacian on the half-line ⋮ Wave propagation speed on fractals ⋮ Estimates for sums and gaps of eigenvalues of Laplacians on measure spaces ⋮ Weak damped wave equations defined by a class of self-similar measures with overlaps ⋮ Spectral asymptotics of Laplacians associated with a class of higher-dimensional graph-directed self-similar measures ^* ⋮ HEAT EQUATIONS DEFINED BY SELF-SIMILAR MEASURES WITH OVERLAPS ⋮ Stochastic wave equations defined by fractal Laplacians on Cantor-like sets

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