Stability for Time Dependent X-ray Transforms and Applications

Alden Waters

Stability for Time Dependent X-ray Transforms and Applications

Analysis of PDEs 2015-10-02 v2

Authors: Alden Waters

Abstract

We prove a logarithmic stability estimate for the time dependent X-ray transform on $\mathbb{R}_t^+\times\mathbb{R}^n$ . To do so, we extend a known result by Begmatov for the stability of the time dependent X-ray transform in $\mathbb{R}^+_t\times\mathbb{R}^2$ . We give some examples of stability and injectivity results in relationship to the Dirichlet-to-Neumann problem. In particular, under the Geometric Control Condtion, we derive inverse logarithmic stability estimates for time dependent conformal factors.

Keywords

inverse problems stability theory stability analysis

Cite

@article{arxiv.1311.1591,
  title  = {Stability for Time Dependent X-ray Transforms and Applications},
  author = {Alden Waters},
  journal= {arXiv preprint arXiv:1311.1591},
  year   = {2015}
}

Comments

this arxiv submission has been split into two separate submissions by separate authors, http://arxiv.org/abs/1406.4854 and the current version. the new version contains a extension to conformal factors

Related papers

View all related →