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Schrodinger equations defined by a class of self-similar measures

Sze-Man Ngai Wei Tang Hunan First Normal University

Analysis of PDEs mathscidoc:2108.03002

2021.7
We study linear and nonlinear Schrodinger equations de fined by fractal measures. Under the assumption that the Laplacian has compact resolvent, we prove that there exists a uniqueness weak solution for a linear Schrodinger equation, and then use it to obtain the existence and uniqueness of weak solution of a nonlinear Schrodinger equation. We prove that for a class of self-similar measures on R with overlaps, the Schrodinger equations can be discretized so that the finite element method can be applied to obtain approximate solutions. We also prove that the numerical solutions converge to the actual solution and obtain the rate of convergence.
Fractal; Laplacian; wave equation; self-similar measure with overlaps.
[ Download ] [ 2021-08-16 10:33:30 uploaded by WeiTang ] [ 1075 downloads ] [ 0 comments ] 
@inproceedings{sze-man2021schrodinger,
  title={Schrodinger equations defined by a class of self-similar measures},
  author={Sze-Man Ngai, and Wei Tang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210816103330370409858},
  year={2021},
}
Sze-Man Ngai, and Wei Tang. Schrodinger equations defined by a class of self-similar measures. 2021. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210816103330370409858.
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