Stochastic Wave Equations defined by Fractal Laplacians on Cantor-like Sets
Probability
2019-10-21 v1
Abstract
We study stochastic wave equations in the sense of Walsh defined by fractal Laplacians on Cantor-like sets. For this purpose, we give an improved estimate on the uniform norm of eigenfunctions and approximate the wave propagator using the resolvent density. Afterwards, we establish existence and uniqueness of mild solutions to stochastic wave equations provided some Lipschitz and linear growth conditions. We prove H\"older continuity in space and time and compute the H\"older exponents. Moreover, we are concerned with the phenomenon of weak intermittency.
Keywords
Cite
@article{arxiv.1910.08378,
title = {Stochastic Wave Equations defined by Fractal Laplacians on Cantor-like Sets},
author = {Tim Ehnes},
journal= {arXiv preprint arXiv:1910.08378},
year = {2019}
}
Comments
34 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1902.02175